I'm currently dating a Chinese girl and her parents have no problem with it whatsoever, in fact I think her mom likes me. My parents, well actually just my mom, has a problem with it. My big brother also has a chinese girlfriend which he's been going out with for like 4 years now.
My mom always wanted to have a blond/blue-eyed baby boy, and I was that boy, only now she says my kids will have none of my features and will look almost entirely asian.
I have no quarrel whatsoever with what my kids will look like (IF I get serious with this girl) BUT, I do happen to believe that a person's personality is, to a certain point, affected by his or her DNA. If I have a kid, let's say a boy, with a chinese woman, I think his DNA structure (which will be more asian than white, even if he has both our genes) would have a tendency to shape his personality not unlike some comon traits most asian guys have. I don't think it's a coincidence that 90% of the asian guys are sort of insecure (NOT always), always talk about fast cars and love making money/are materialistic, etc.
I wouldn't want my kid to be like that as I think that isn't a good way of life in general.
This is just a hunch really, I'm not sure how much DNA affects personality and wether or not the part of your DNA that does would be lost if most of the genes you mix are recesive and the other dominant genes take over. But basically, I think a half-asian/half-caucasian child would perhaps relate better to his asian heritage.