Addressing "Whether the Mother of God was a virgin in conceiving Christ?," St. Thomas Aquinas gives the following objection in his Summa Theologica III q. 28 a. 1 arg. 4:
…things of the same species have the same mode of generation [i.e., procreation; e.g., cats make cats in the same way; humans make humans in the same way; etc.]: since generation is specified by its terminus [end] just as are other motions. But Christ belonged to the same species as other men, according to Phil. 2:7: "Being made in the likeness of men, and in habit found as a man." Since therefore other men are begotten of the mingling of male and female, it seems that Christ was begotten in the same manner…
To which he responds (ad 4):
This argument is true of those things which come into existence by the way of nature: since nature, just as it is fixed to one particular effect, so it is determinate to one mode of producing that effect. But as the supernatural power of God extends to the infinite: just as it is not determinate to one effect, so neither is it determinate to one mode of producing any effect whatever. Consequently, just as it was possible for the first man to be produced, by the Divine power, "from the slime of the earth," so too was it possible for Christ's body to be made, by Divine power, from a virgin without the seed of the male.
Notice that he says "without the seed (semine) of the male"—thus, without St. Joseph's DNA. But that doesn't necessarily imply Jesus only had half the chromosomes of other humans.