What is Man? Karl Barth solves this enigmatic anthropological question with one word: Jesus! Barth fleshes out his anthropology throughout The Church Dogmatics, Vol. 3.2, Sections 45-46: The Doctrine of Creation (CD III/2), beginning with Jesus, Man for Other Men in "§45 Man in His Determination as the Covenant-Partner of God" where Barth declares the victory of the Crucified One over the Dionysus of Nietzsche's Man in Freedom. Barth shifts from the truest expression of anthropology in Jesus Christ to the anthropology of us all in following section: "§46 Man as Soul and Body" where Barth defines our anthropology by the famous phrase "Soul of my Body" as exemplified in the header to this section:
Through the Spirit of God, man is the subject, form and life of a substantial organism, the soul of his body—wholly and simultaneously both, in ineffaceable difference, inseparable unity, and indestructible order.
Barth, Karl. Church Dogmatics III.2 The Doctrine of Creation. Trans. G. W. Bromiley, J. W. Edwards, O. Bussey, Harold Knight, J.K.S. Reid, R.H. Fuller, R.J. Ehrlich, A.T. Mackey, T.H.L. Parker, H.A. Kennedy, J. Marks. Vol. 15. London: T & T Clark, 2009. 119. Print. Study Edition. 
Soul of My Body
In this phrase, "Soul of My Body", Barth affirms the dichotomy vernacular of ancient orthodoxy by defining Man in two parts: Body and Soul. Barth's dichotomy of "Soul of My Body" reinforces the inseparability of these two parts as exemplified in the header to §46 Man as Soul and Body where this phrase, Soul of My Body, is terminologically reminiscent of the Chalcedon Christological formulation of the two natures of Jesus as "inconfusedly, unchangeably, indivisibly, inseparably." However, Barth's affirmation of dichotomy is a "yes, but..." because Barth affirms trichotomist, dichotomist and monistic anthropologies and yet denies them all as he strikes out into his own definition in his "Soul of My Body" anthropology.
For a concise summary of Barth's anthropology, the follow quotation from the conclusion of §46 Man as Soul and Body is clarifying:
Our interpretation of those phenomena, formulated as briefly as possible in four propositions would be as follows.
- The soul does not act on the body, but the one man acts. And he does it in that as soul he animates himself and is acting subject, but always as soul is soul of his body, animated by himself, determined and enabled to act, and engaged in action.
- Again, the soul does not suffer from the body, but the one man suffers. And this takes place in that as soul (namely, as acting subject) he is fundamentally exposed and susceptible to such hindrances and injuries, but as soul of his body must actually experience them.
- Again, the body does not act on the soul, but the one man acts. He acts in that as body he is animated by himself, determined and enabled to act, and engaged in action, but as body of his soul, animating himself and acting subject.
- And again, the body does not suffer from the soul, but the one man suffers. When this takes place, it means that as body he really experiences such hindrances and injuries, but that as body of his soul he must really make them his own.
The one whole man is thus one who both acts through himself and suffers in himself, but always in such a way that he is first soul (ruling, in the subject) and then body (serving, in the object)--always in this inner order, rationally and logically of his whole nature.
Ibid. 223-4. [432-3]
Monism: Embodied Soul and Besouled Body
The positive Monistic elements of Barth's anthropology is in his identification of the man Jesus of Nazareth as our true anthropology, and in the inseperability of the Soul and Body of every person. Barth describes the indivisible unity of Man's two parts by this in the dialectical phrase: "embodied soul and besouled body" as exemplified in the following quote:
The Jesus of the New Testament is supremely true man in the very fact that He does not conform to the later definition, and far from existing as the union of two parts of two "substances," He is one whole man, embodied soul and besouled body: the one in the other and never merely beside it; the one never without the other but only with it, and in it present, active and significant; the one with all its attributes always to be taken as seriously as the other. As this one whole man, and therefore as true man, the Jesus of the New Testament is born and lives and suffers and dies and is raised again.
Ibid. 121 
Dichotomy: The Spirit that unifies Soul and Body
Karl Barth identifies the spirit with the Spirit of God. The Spirit is not another part of man. Man exists in a dichotomy of two parts: Body and Soul, and the Spirit of God is what brings to life the Soul of My Body. Man exists because he has Spirit. Barth explains the relationship of the Holy Spirit to Man's Soul of His Body as follows:
Our statement that man is wholly and at the same time both soul and body presupposes the first statement that man is as he has Spirit. We said in our second sub-section [46.2] that it is the Spirit, i.e., the immediate action of God Himself, which grounds, constitutes and maintains man as soul of his body. It is thus the Spirit that unifies him and holds him together as soul and body. If we abstract from the Spirit and therefore from the act of the living Creator, we necessarily abstract between soul and body. If we consider man for himself, i.e., without considering that he is only as God is for him, he is seen as a puzzling duality, his mortal body on the one side and his immortal soul on the other, a totality composed of two parts inadequately glued together, of two obviously different and conflicting substances. And however much we then try to persuade ourselves that this duality is the one man, we stand in the midst of Greek and every other form of heathenism, which sees neither the real God nor real man, and cannot do so, because knowledge of the Spirit is needed for this purpose and this is incompatible with heathenism. Our only relief will then be found in the see-saw movement between ideas and appearance, thinking and speculation and so on, which pervades the history of philosophy in every age.
Ibid. 186. 
The Spirit is Identical With God, Not A Part of Man
The Spirit is the Holy Spirit, and it is the Spirit that makes creation alive, as it is so panentheistically expressed in Acts 17:28: in Him we live and move and have our being. Barth differentiates himself from Pantheism because he does not believe that Creation is in God, but it is the Spirit that is in Creation and brings it into being. It is the movement of the Creator Spiritus towards Creation that makes all things alive, and there is no life or suffering that exists apart from the animation of the Spirit as the next quotation explains:
We thus understand the statement that man has spirit and is thereby man as equivalent in content to our first statement, that he is man, and therefore soul of his body, not without God but by God, i.e., by the ever new act of God. Spirit is, in the most general sense, the operation of God upon His creation, and especially the movement of God towards man. Spirit is thus the principle of man's relation to God, of man's fellowship with Him. This relation and fellowship cannot proceed from man himself, for God is his Creator and he His creature. He himself cannot be its principle. . . . This is what is meant when Scripture says of man that he has spirit or the Spirit, or that he has done this or that in the Spirit or through the Spirit, or has said or done or suffered from the Spirit. This never signifies a capacity or ability of his own nature, but always one originally foreign to his nature which has come to it from God and has thus been specially imparted to it in a special movement of God towards him. . . . The Spirit, in so far as He not only comes but proceeds from God Himself, is identical with God.
Ibid. 149 [355-6]
Barth includes a fascinating discussion about how evil spirits are not excluded from what is given to man from the Spirit:
God remains free to give, to take, and to give again. He shows Himself free in the fact that He can also give an evil spirit to man--this too is a kind of commission imposed on the man concerned--as again with Saul (1 Sam 16:14f) and in 2 King 19:7 with the king of Assur; and it can again happen (1 Sam 16:23) that this evil spirit too can depart from him. Even the "lying spirit in the mouth of all false prophets" is, as we are told in the remarkable passage in 1 King 22:21f, one of the spirits that surround the throne of Yahweh, and it is called and empowered by Yahweh Himself for the infatuation of Ahab. There are other passages (Isa 4:4,40:7;Job 4:9) where the Spirit is the burning blast of divine judgment, a power of destruction and extermination. Hence we cannot be surprised to hear in Job 20:3 of a spirit "without insight" (Zurich Bible), in Isa 29:24 of an "erring spirit," in Zech 13:2 of an "unclean spirit"; and even in the New Testament of a "spirit of bondage" (Rom 8:15), of "another spirit" which presents another Jesus and another gospel (2 Cor 11:4); and further, with a frequency which cannot be disregarded, of evil spirits, unclean spirits and spirits that cause sickness, with all the work of these spirits in and upon men. If God condemns a man and through him other men, He can give him such a spirit.
Ibid. 151. [357-8]
In the previous section, Barth's Anthropology is nearest to the traditional Dichotomists, because he believes that man is constituted in two parts: Body and Soul. Barth does not believe that the spirit is a third part of man, because he identifies the spirit with the Spirit of God. The Creator Spiritus movement towards man is the basis of his life as he exists in his "Soul of My Body."
1 Thess 5:21 is the locus classicus for trichotomy because it contains the phrase "spirit and soul and body" suggesting Man exists in three parts. Barth has an excellent comment on this verse so often used to justify trichotomy by Greek apologists:
The only biblical passage which can be regarded as ambiguous in this regard is 1 Thess 5:23 . . . Scripture never says "soul" where only "spirit" can be meant. But it often says "spirit" where "soul" is meant; and there is inner reason for this in the fact that the constitution of man as soul and body cannot be fully and exactly described without thinking first and foremost of the spirit as its proper basis. We are nowhere invited to think of these three entities. Even Augustine, when he once gave the almost intolerably harsh formulation: there are three things which define a human being: spirit, soul and body, immediately corrected himself: these may, on the other hand, be called two, since often the soul is named together with the spirit. Trichotomism must necessarily issue in the view and concept of two different souls and therefore in a splitting of man's being. This makes understandable the force with which it was condemned at the Fourth Council of Constantinople in A.D. 869-70.
Ibid. 148-9 
Barth is famous for his relentless rejection of Natural Revelation and "non-theological" Anthropology is no exception. Man is unable to know thyself apart from the Word of God and any such non-theological anthropology is a dangerous foe of Christian anthropology. Barth believes the results of non-theological anthropology are hypothetical and non-essential, yet he does not prohibit all non-theological anthropological investigations. Wolfhart Pannenberg's Anthropology in Theological Perspective may be an example of a scientific and theological book on anthropology that meets Barth's qualifications for a scientific and yet theological anthropology. Barth believes that non-theological anthropology collapses in atheistic dogma as the following quotation exemplifies:
It is clear that we must here depart from the way taken by the anthropology which sets itself the aim of understanding man without God. It is of the essence of every non-theological anthropology to set itself some such aim. Of course, it is not essential that this aim be set absolutely and so be intended in the sense of atheistic dogma. It can be intended only hypothetically.
Ibid. 139 [346-7]
To summarize, Karl Barth's anthropology may be identified as Jesus Christ in particular, and as "Soul of My Body" in general. Man exists in two parts: Soul and Body. These two parts are inseparably unified by his phrase, "Soul of My Body". The spirit is not a third part of man, but is identified with the Spirit of God, and it is through the Spirit's free movement towards Man and through Man that Man is brought to life by the operation of God by his Spirit in Creation. Man does not pantheistically exist in God, but there is no life apart from through the Spirit.
Header Background Image: "Illustrations to Robert Blair's The Grave: The Soul Hovering over the Body" by William Blake - http://www.blakearchive.org/exist/blake/archive/work.xq?workid=bb435&java=no. Licensed under Public Domain via Wikimedia Commons.