Objection 1. It would seem that spiritual relationship does not pass from husband to wife. For spiritual and bodily union are disparate and differ generically. Therefore carnal union which is between husband and wife cannot be the means of contracting a spiritual relationship.
Objection 2. Further, the godfather and godmother have more in common in the spiritual birth that is the cause of spiritual relationship, than a husband, who is godfather, has with his wife. Now godfather and godmother do not hereby contract spiritual relationship. Therefore neither does a wife contract a spiritual relationship through her husband being godfather to someone.
Objection 3. Further, it may happen that the husband is baptized, and his wife not, for instance when he is converted from unbelief without his wife being converted. Now spiritual relationship cannot be contracted by one who is not baptized. Therefore it does not always pass from husband to wife.
Objection 4. Further, husband and wife together can raise a person from the sacred font, since no law forbids it. If therefore spiritual relationship passed from husband to wife, it would follow that each of them is twice godfather or godmother of the same individual: which is absurd.
On the contrary, Spiritual goods are more communicable than bodily goods. But the bodily consanguinity of the husband passes to his wife by affinity. Much more therefore does spiritual relationship.
I answer that, A may become co-parent with B in two ways. First, by the act of another (B), who baptizes A's child, or raises him in Baptism. In this way spiritual relationship does not pass from husband to wife, unless perchance it be his wife's child, for then she contracts spiritual relationship directly, even as her husband. Secondly, by his own act, for instance when he raises B's child from the sacred font, and thus spiritual relationship passes to the wife if he has already had carnal knowledge of her, but not if the marriage be not yet consummated, since they are not as yet made one flesh: and this is by way of a kind of affinity; wherefore it would seem on the same grounds to pass to a woman of whom he has carnal knowledge, though she be not his wife. Hence the verse: "I may not marry my own child's godmother, nor the mother of my godchild: but I may marry the godmother of my wife's child."
Reply to Objection 1. From the fact that corporal and spiritual union differ generically we may conclude that the one is not the other, but not that the one cannot cause the other, since things of different genera sometimes cause one another either directly or indirectly.
Reply to Objection 2. The godfather and godmother of the same person are not united in that person's spiritual birth save accidentally, since one of them would be self-sufficient for the purpose. Hence it does not follow from this that any spiritual relationship results between them whereby they are hindered from marrying one another. Hence the verse:
"Of two co-parents one is always spiritual, the other carnal: this rule is infallible."
On the other hand, marriage by itself makes husband and wife one flesh: wherefore the comparison fails.
Reply to Objection 3. If the wife be not baptized, the spiritual relationship will not reach her, because she is not a fit subject, and not because spiritual relationship cannot pass from husband to wife through marriage.
Reply to Objection 4. Since no spiritual relationship results between godfather and godmother, nothing prevents husband and wife from raising together someone from the sacred font. Nor is it absurd that the wife become twice godmother of the same person from different causes, just as it is possible for her to be connected in carnal relationship both by affinity and consanguinity to the same person.
Source: Summa Theologica (New Advent)