An interesting thing I noticed about some foreigners or recent immigrants in the United States is that they don't quite see 'race' the same way Americans to. For example, I've met some Asian visitors who would see as "white" someone whom most Americans would categorize as 'black'. For example, some of my Asian friends saw a lighter-skinned, straight-haired "black" woman as "white." They also saw a "black man" with lighter skin and a high, narrow nose as "mixed", not "black". A black acquaintance (not the 'miscategorized' persons - who were actually just images appearing in print and film media) was quite flabbergasted that these aliens could not see what was 'clear' to most Americans - that these folks were 'black'. But I don't think the foreigners really meant any harm. It was a case of, "Well, she had some African features but since she had more European features, I thought she was European American." They just don't see 'race' the way we do.
The same goes with how some other individuals of mixed descent. I've encountered people from Asia who see Jennifer Lopez - as well as other mestizo Mexicans - as 'white European'.
I'm not saying if that's a 'right way' or 'wrong way' to see things. In fact, it is the opinion of some people that we should be colorblind and not notice physical differences between populations at all, and that in an ideal world, we should not even be discussing 'race'. I'm not getting into that argument - there are many who argue eloquently already - but I thought it is interesting to share this observation that there's not one absolute way of looking at 'race'.