Does he though? When he died on the cross he died as a man. Surely he ceased to be incarnate at that point and returned to being purely divine? Does he still have a human soul?
He continued to be Incarnate and in fact resumed His Body at the time of His Resurrection. Remember Doubting Thomas?
St John 20:19 Now when it was late that same day, the first of the week, and the doors were shut, where the disciples were gathered together, for fear of the Jews, Jesus came and stood in the midst, and said to them: Peace be to you.
20 And when he had said this, he shewed them his hands and his side. The disciples therefore were glad, when they saw the Lord…
24 Now Thomas, one of the twelve, who is called Didymus, was not with them when Jesus came.
25 The other disciples therefore said to him: We have seen the Lord. But he said to them: Except I shall see in his hands the print of the nails, and put my finger into the place of the nails, and put my hand into his side, I will not believe.
26 And after eight days again his disciples were within, and Thomas with them. Jesus cometh, the doors being shut, and stood in the midst, and said: Peace be to you.
27 Then he saith to Thomas: Put in thy finger hither, and see my hands; and bring hither thy hand, and put it into my side; and be not faithless, but believing.