You have to take into account at the same time two dogmas, namely those on:
Incarnation (if considered on fieri) or Hypostatic Union (if considered in esse), and
According to the first, the Incarnate Word has two substances or natures, the divine and the human, united in one divine Person. BTW, the first definition of the 5th Ecumenical Council of Constantinople 553 explicitely identifies ousía (substantia) with physis (natura) and hypostasis (subsistentia) with prosopon (persona) .
According to the second, the substance of the bread is converted into the substance of the body of Christ. Regarding this:
a. Since the body of any living animal (including humans) is not dry but permeated by blood, the substance of the bread is actually converted into the substance of the irrigated body of Christ, i.e. his body, as abstracted in a dry state, and his blood.
b. Since the body of any living human being is infused by a spiritual soul, the consecrated host, being the body of Jesus Christ, is infused by his spiritual soul. But the substance of the bread has not been converted into the substance of the soul. So, one does not eat directly the soul but the body infused by the soul, just as someone who hugs you does not hug your soul but your body infused by your soul.
To note, the previous two points would also be the case if the bread were transubstantiated into the body of any ordinary human person, something which God could perfectly do but which of course there would be no point in doing. I point this out to emphasize that transubstantiation has nothing to do with Jesus' body having any special property after his resurrection, as Lutherans claim about their "sacramental union". This should already be clear from the fact that the first transubstantiation occurred at the Last Supper while Jesus' body was in a passible state.
c. The soul  of Jesus Christ is united to his divine Person or Hypostasis, Who, as Any of the three divine Persons, is the one and only divine substance or nature.
So, just as St. Mary hugging baby Jesus was not hugging the substance of the Father but the Son of God in his assumed human nature, (speaking even more strictly, she was hugging his body, which was infused by his soul just as any living human body, with Jesus' soul being in turn hypostatically united to his divine Person,) a person receiving Communion does not eat the divine substance but the body of Jesus, which is infused by his soul, which is hypostatically united to his divine Person, Who, as Any of the three divine Persons, is the one and only divine substance or nature.
 Pavouris, Raphael (2001), The condemnation of the Christology of the three chapters in its historical and doctrinal context: the assessment and judgement of Emperor Justinian and the Fifth Ecumenical Council (553). PhD thesis, University of Glasgow.
 St. Thomas Aquinas, Summa Theologica, III, q.6, a.1, "Whether the Son of God assumed flesh through the medium of the soul?"