Objection 1. It would seem that the Person of Christ is not composite. For the Person of Christ is naught else than the Person or hypostasis of the Word, as appears from what has been said (2). But in the Word, Person and Nature do not differ, as appears from I, 39, 1]. Therefore since the Nature of the Word is simple, as was shown above (I, 3, 7), it is impossible that the Person of Christ be composite.
Objection 2. Further, all composition requires parts. But the Divine Nature is incompatible with the notion of a part, for every part implicates the notion of imperfection. Therefore it is impossible that the Person of Christ be composed of two natures.
Objection 3. Further, what is composed of others would seem to be homogeneous with them, as from bodies only a body can be composed. Therefore if there is anything in Christ composed of the two natures, it follows that this will not be a person but a nature; and hence the union in Christ will take place in the nature, which is contrary to 2].
On the contrary, Damascene says (De Fide Orth. iii, 3,4,5), "In the Lord Jesus Christ we acknowledge two natures, but one hypostasis composed from both."
I answer that, The Person or hypostasis of Christ may be viewed in two ways. First as it is in itself, and thus it is altogether simple, even as the Nature of the Word. Secondly, in the aspect of person or hypostasis to which it belongs to subsist in a nature; and thus the Person of Christ subsists in two natures. Hence though there is one subsisting being in Him, yet there are different aspects of subsistence, and hence He is said to be a composite person, insomuch as one being subsists in two.
And thereby the solution to the first is clear.
Reply to Objection 2. This composition of a person from natures is not so called on account of parts, but by reason of number, even as that in which two things concur may be said to be composed of them.
Reply to Objection 3. It is not verified in every composition, that the thing composed is homogeneous with its component parts, but only in the parts of a continuous thing; for the continuous is composed solely of continuous [parts]. But an animal is composed of soul and body, and neither of these is an animal.
Source: Summa Theologica (New Advent)