To add to u/Yazman’s answer, I can talk a bit about the other end of the Mediterranean in the crusader states. There, Catholic and Orthodox could certainly marry. Fulcher of Chartres, who chronicled the First Crusade and then remained in the east for the rest of his life, wrote that:

“…we who were Occidentals have now become Orientals…Some have taken wives not only of their own people but Syrians or Armenians or even Saracens who have obtained the grace of baptism...He who was born a stranger is now as one born here; he who was born an alien has become as a native.” (Fulcher of Chartres, pg. 271)

So apparently crusaders in the east could also marry Muslims (Saracens), if they had converted to Christianity. But what if one spouse was a Muslim and one a Christian? Well, interfaith marriages had been forbidden by the church long before - even going back to the 4th century, church councils had prohibited marriages between first Christians and pagans, then Christians and Jews, and these laws were adopted by secular Roman law as well. By the time of the crusades, laws prohibiting marriage between Christians and pagans/Jews were incorporated into Gratian’s Decretum, and they were now interpreted to refer to Muslims as well.

Seems simple…Christians could not marry Muslims, full stop! But it’s not so simple. The secular laws of crusader Jerusalem state that they have no jurisdiction over marriage itself, which was up to the church, but they did have jurisdiction over other matters that resulted from a marriage, such as property and inheritance disputes. One spouse was entitled to half of the couple’s possessions if the other spouse died, unless one spouse was a Muslim, because Muslims weren’t allowed to inherit property from Christians. Why would that have to be prohibited specifically, if Muslims and Christians never married? This might mean that they did marry after all. Such a marriage would certainly be invalid according to the church, but apparently it may not have been illicit under secular law. In other words, was being a Muslim an impediment to marriage, or not? The church might have looked the other way as long as there were no property or inheritance issues.

The laws also dealt with the question of what to do when one spouse converted after marriage. A spouse could convert to Christianity after marriage, so evidently they must have been able to get married without being Christian first. What if they converted to Islam after marriage? Did the marriage then become invalid? If both spouses were Christian, but then one spouse apostatized, i.e. they converted to Islam and then ran away, could the other spouse marry someone else? What if the apostate spouse changed their mind and came back? These are the sorts of questions the secular and ecclesiastical authorities in Jerusalem worried about. They generally felt that apostasy didn't make the marriage invalid, because the apostate spouse was still alive and might return someday.

For marriages between Christians and Muslims, we don’t know how often that actually happened. The only example I can think of is a story from Usama ibn Munqidh, an author from Damascus who often visited crusader Jerusalem. He mentions a Muslim man whose mother was Muslim, but whose father was “a Frank”, a crusader. The mother had killed the father, and the mother and son then became bandits who attacked Christian pilgrims. The son was eventually caught and subjected to a trial by water, which Usama describes in detail as an absolutely crazy nonsensical Frankish custom. Unfortunately we don’t know anything else about the man’s father, but in Usama's mind, the interfaith marriage wasn't the most unusual part of this story, so maybe it was a relatively normal thing.

Among the nobility, I can’t think of any instance where a crusader noble married a Muslim. There was supposedly some discussion during the Third Crusade about Richard the Lionheart’s sister marrying Saladin’s brother, but that’s probably completely legendary or rumours meant to slander Richard. Otherwise, the crusader nobility rarely ever interacted with the Muslim population at all so they never intermarried.

But among the lower classes, the merchants and tradespeople, it apparently did happen (or at least, could have theoretically happened).

Sources:

Fulcher of Chartres, A History of the Expedition to Jerusalem, 1095-1127, trans. Frances Rita Ryan, ed. Harold S. Fink (University of Tennessee Press, 1969)

Usama ibn Munqidh, The Book of Contemplation: Islam and the Crusades, trans. Paul M. Cobb (Penguin, 2008)

James A. Brundage, "Marriage law in the Latin Kingdom of Jerusalem", in Outremer: Studies in the History of the Crusading Kingdom of Jerusalem, ed. B. Kedar, H. Mayer, R. Smail (Jerusalem, 1982)

Marwan Nader, "Urban Muslims, Latin laws, and legal institutions in the Kingdom of Jerusalem", in Medieval Encounters 13 (2007)

So I've written an answer addressing inter-faith marriage in al-Andalus during the Umayyad years here. At least as far as al-Andalus goes, this should answer your question. The short answer is that, yes, inter-faith marriages did happen, although certain combinations of religions & sexes were more "common" than others.

If you're interested in some more general stuff about other religions in Andalusi society, I'll list a few other relevant posts I've made below.

I wrote about how christianity & nobility overlapped in that era, I've written an answer about that here. I also talked about that a bit here.

And if you're interested in how other religions were restricted in that era, see this post.

If you have any followup questions, let me know.