I believe I might be able to provide some insight from a male's perspective here.
Although i'm born and raised canadian, (heck i'm listening to aerosmith now), my parents are caribbean giving me a tanned complexion. By the time I was 21, I already spent 9 years in long term relationships with girls of another race than my own. (either white or asian). Since I was 21 i've dated (both casually and seriously) a good 80-100 girls of mixed races. (i.E. British, australian, canadian, italian, portuguese, irish, american, chinese, etc.) i've never dated a girl my own race.. Ever. (go figure)
anyway, my parents are fine with me dating girls of almost any race.. (save for blacks). I've been in relationships where the parents didn't agree with me for one reason or another.
There are two things which need to be understood here. Number one is, your family is very important and their opinions do matter. They are from another time where this multicultural society didn't exist... All this multiculturalism is very very recent. Their ideals and morals are different, and there is nothing wrong with this. It's not racism, it's preference based on their own life experiences and upbringing. You can't blame them for feeling this way. It can even be threatening to them, or shameful to extended family members (aunts, uncles, grandparents, etc.)
if your parents don't agree with it and you know they never will... Then honestly, you have a big decision to make. The family stress will hinder your relationship on various levels. It will cause problems and bring you down from what would normally be a healthy relationship. This weight on your shoulders will be with you all the time. Imagine the tension if you two ever got married. If you cry on your wedding, it should be tears of joy.
However, it's possible for some parents to come around. Eventually i've always been accepted by parents. Typically because I come from a decent family, very well raised, I work hard, and do well in school. All these influces usually rub off on their daughter and sooner or later I hear praises on how well she's doing in school, how much she calmed down, how much more polite she is, or how they've never seen her reading a book for fun before. Usually when they make this association of the boyfriend being a positive influence on their daughter, they seem to lighten up. It also helps that I made an effort to learn more about their culture, or to be a positive part of their lives. In the end, it always worked out for me... So it is possible for parents to come around. But as I said, some parents are predisposed to other thoughts and changing that can prove very difficult if not impossible.
I think there is nothing wrong with multicultural children, some are very beautiful. And I like the idea of children being raised without this bias towards a single culture (their own) but being more open to the world. On the other hand, i'd like if some people also retained some "purebred" children. Cultures are important to keep too, they are our roots.