Jehanne, the Church has never said anything against interracial marriages officially, but that doesn't mean they're necessarily a good idea. We are free to make bad marriages within the Church. But I suppose you can't say that an interracial marriage is bad in itself, or that all of them are bad, as a general rule.
However, I have read -- from a secular book, so take it with a grain of salt -- that interracial marriages and even interracial fornicaton was punished severely by the Spanish Church when they were colonizing America, that a stricter contingent within the Church did not want inter-marrying with natives. I'm not sure if that's true or not. Some people think that the Spaniards marrying the natives was a civilizing factor in itself, and I can't really say that I have an opinion either way.
All I know is that personally, I probably wouldn't do it. I find them odd myself, and I grew up in a very mixed-race environment. If I were marrying an Asian woman, I wouldn't trust myself to know whether it was a fetish or true love. Also, I'd just prefer to have all-white children.
Has anyone wondered this -- why is it almost always white women with black men, and white men with Asians? It is much, much more rare to see white women with Asian men, or white men with black women. There just feels like something wrong with that to me, something about breaking taboos, something physical and not spiritual. I also see tons of white women with Hispanics these days.
As Matthew said, in this country, it is liberalism that ties people together. But I don't want my kid to be culturally tied together by that. Even if the kid were raised Catholic, isn't there a risk that, being mixed-race, he would feel more at home in the multicultural American stew and would begin thinking in a liberal way? Of course, there's always a risk with any Catholic kid that they will be seduced by the world, but in this case, I could see a mixed-race child seeking IDENTITY in this way, while a white person wouldn't.
The point of my post is that, though they happened often in the past, like in Italy with the Moors, mixed-race marriages seem to have been fairly unheard-of in the late Middle Ages through the Renaissance and beyond in Europe ( though I could be wrong. ) Therefore, in modern times, they strike me as a very American phenomenon. One that we have, as usual, exported around the world. Though there's no proof, and no official word from the Church, I think it's a general sign of decay, a symbol of the replacement of the Old European Catholic world by the New ʝʊdɛօ-Masonic American world.