Heritage? I'm not sure how this is defined in today's day and age. Genghis Khan and the Mongols conquered Northern /Southern China and pretty much the entire Asia. Troops and merchants were sent to Afghanistan, Persia, Azerbaijan, Armenia and Eastern Europe. As far as the history tells, anyone from the above region can very well be part Chinese/Mongol, even though minute.
http://www.fsmitha.com/h3/h11mon.htm
I'm part Dutch from my mother's side from 3 generations ago. My wife is part English from her mother's side as well. Although I wasn't born in the U.S. but I have lived here much longer than I had in my birth country - Taiwan.
My two boys were born Ameican citizen and that's what they are. I'm not Taiwanese-American, Taiwanese-Chinese or even Chinese-American. I do not have dual citizenship and I have sworn as an American citizen some 18 or 19 year ago. I have had friends of all races growing up in Southern CA. It wasn't evident until my family moved out to the Mid West then we realized we ARE the minority.
I remember going to a Starbucks in the Indy area three years ago. As soon as we walked in, we immediately drew everyone's attention. Some were friendly and some were...well, not so friendly. One parent pulled her kids from the sitting area as we walked pass.
Another time at a shopping mall in Indy, I was pushing my son in the stroller and a friendly older gentleman asked how old my son was. Well, he literally spelled it out, "H_o_w o_l_ d i_s y_o_u_r b_o_y? He assumed I didn't speak English or couldn't speak it well. It didn't offend me and I replied how old my son was.
It's very likely my sons will come home one day with some cute little blond, redhead or brunette. My grand children will likely bare little resemblance of their Asian heritage. Some of my mom's friends have grand kids with blond hair and blue eyes. Another one or two generations after the only way to tell is perhaps through the family name. Then again, that can be legally changed, too.
Only heritage we need to know is that we are all Homo Sapiens.