You can explain to him that skin color isn't everything - that to a Japanese person, for example, it might be very insulting to be called Chinese, that we don't know people's heritage, and so it's polite to not comment on what YOU think their ethnicity might be. And to someone who is a 4th-generation American, being called "that Chinese lady" may make her think "Am I not considered American yet? How long do I have to live here, anyway!"

People are so much more than their skin color.

He is blessed to have different skin-colors in his family, but lots of people aren't, so it is best not to use that as something to talk about without getting to know that person.