Selected Reform Responsa 191
This is discussed in the Talmud , Kiddushin 66b-67a . Rashi there explains why, in general, in normal marriages the child follows the status of the father rather than that of the mother. He bases it on Scripture, the first chapter of the Book of Numbers , which says a number of times that the Children of Israel shall be numbered according to their father’s house.
There is also a second consideration. The fertilized ovum is carried in the womb of the wife for full term. Does the fact that the body matures in the womb of the wife have any bearing on the status of the child? It does, definitely. This can be seen from the special case of a pregnant proselyte. A woman became pregnant while a Christian (presumably pregnant by a Christian man). During her pregnancy, she becomes converted to Judaism . After her conversion, her child is born. What is the status of the child? Is it a Gentile who needs to be converted, since both parents were Gentile? The answer of the overwhelming number of authorities on this matter is that the child is part of the mother's body and the conversion ritual(the mikvah) converts not only the mother, but the child that she is carrying(see the authorities cited in the responsum, "The Pregnant Proselyte," in Modern Reform Responsa, pp. 143 ff).
While the situation here is far different from normal marriage, the attitude of the law to normal marriage may serve as an analogy in this special situation. Since the tendency of the law is to emphasize the influence of paternity, and since the wife carries the child and, therefore, according to the law her status impresses itself upon the child, these constitute two reasons why the child here in question should be considered the offspring of the married couple. Of course, as has been said, the situation is unusual, but the likelihood is that as the study of this problem develops, the tendency of the law will likely be to reach the above conclusion.
Solomon B. Freehof