The woman converted to the man's faith.

...But that's boring, simplistic, and doesn't actually help us understand either interreligious dynamics in the Middle Ages or individual people's lives. So let's do better.

It's important to keep in mind that in the Middle Ages, marriage fell under religious law, not secular--there was no going to the medieval equivalent of a town hall to say vows before a justice of the peace. This meant laws about who could marry each other were up to the leaders and lawmakers of each faith tradition--in the European Middle Ages, the context for my answer, primarily Islam, Judaism, and Latin Christianity.

And in general, those leaders were not pleased with the idea of interreligious marriage. In Christianity and Judaism, it wasn't even a question. By long established principle, each religion's law applied only to those of the same faith tradition. A Christian and a Jew could not marry each other because there was no single authority to validate the union. Islamic law did permit and recognize marriages between Muslim men and non-Muslim women, but not the other way around.

The most famous example of the latter situation comes from early al-Andalus, that is, Iberia right after the Islamic conquest. Muslim victors frequently intermarried with the native Gothic Christian aristocracy; later generations of these families might tout their noble/royal heritage from Christian women over less elite descent from Muslim women.

But in general, we're talking about two pathways for an interreligious partnership of any duration: the conversion of one partner to the other's religion, or sex (and maybe more) outside marriage. In all of these cases, by far the dominant pattern was for the woman to come from a lower-status religion, the man from the higher.

One reason for this was economic. To cross religious lines for a partnership, especially in cases of conversion, frequently resulted in formal or social outcast status from one's original community. Thanks to sexist labor and inheritance laws, men were better equipped to absorb the blow of their wife's loss of financial support (including a dowry) than otherwise. Penalties could likewise be especially severe for women who worked as, or were accused of being, prostitutes.

The other major reason, of course, is sexism. The laws of all three religions could morph around ways to keep women sexually available to men--their own men.

For example, the Sefer Hasidim from 12th century Ashkenaz disagrees so vehemently with the idea of interreligious relationships that it even bans Jews from shaking hands with Gentiles of the other sex. Yes, even with gloves. Scandalous! But VIP Jewish scholar Maimonides asserted against the weight of the Mishnah that a Jewish man could marry his Gentile ex-servant because that was less of a sin than continuing to fornicate with her, outside of marriage. This declaration is less important for any legal purposes related to its own content, and more for what it implicitly recognizes and lets go without commentary: it was bog standard for Jewish men--and Christian and Muslim men, in point of fact--to have sex with/rape their female servants and slaves.

Similar patterns are visible with Islam and Christianity. As I mentioned earlier, Islamic law outright recognized marriages between Muslim men and non-Muslim women. In Christian religious teaching, there was an undercurrent of the tentative acceptability of Christian men entering sexual relationships with non-Christian women, because (the clerical writers hoped) it might lead to the woman's conversion and salvation.

But the reverse could absolutely not be the case, apparently. 14th century canon lawyer Oldradus de Ponte ruled that a Jewish man who attempted to marry a Christian woman could be condemned to death under laws against adultery. Even a case not involving marriage or rape ought to incur a punishment like castration.

And unfortunately, as I've discussed in earlier answers, it was also accepted and endorsed that victorious soldiers could and would rape women (and sometimes children) in towns and lands they conquered. This was as true across religious lines as it was within them.

Interreligious marriages in the Middle Ages, therefore, were a non-starter in almost all cases. And when it came to interreligious sexual encounters or relationships, the legal and social currents in the three major Western religions flowed towards securing women's sexual availability to men.