The union is not in the nature but in the person. There is no change in the nature.
St. Thomas Aquinas wrote in
Summa Theologica, Part 3, Question 2. The mode of union of the Word incarnate, Article 2. Whether the union of Incarnate Word took place in the Person?
Reply to Objection 1. Although in God Nature and Person are not really distinct, yet they have distinct meanings, as was said above, inasmuch as person signifies after the manner of something subsisting. And because human nature is united to the Word, so that the Word subsists in it, and not so that His Nature receives therefrom any addition or change, it follows that the union of human nature to the Word of God took place in the person, and not in the nature.
Article 7. Whether the union of the Divine nature and the human is anything created?
I answer that, The union of which we are speaking is a relation which we consider between the Divine and the human nature, inasmuch as they come together in one Person of the Son of God. Now, as was said above (I, 13, 7), every relation which we consider between God and the creature is really in the creature, by whose change the relation is brought into being; whereas it is not really in God, but only in our way of thinking, since it does not arise from any change in God. And hence we must say that the union of which we are speaking is not really in God, except only in our way of thinking; but in the human nature, which is a creature, it is really. Therefore we must say it is something created.
newadvent.org/summa/4002.htm#article1