You can become a U.S. citizen and maintain citizenship of your country of birth(or others your are holding)if the country wasn't China and a few others listed in the link I have provided.
Half of my immediate family have become U.S. Citizens and maintained their other citizenships.
I was told by a friend who's getting U.S. citizenship you have to take an oath renouncing other citizenship.. here it is:
"“I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen…” from the Oath of Allegiance "
Edit: can you ask your family if they took that oath, or is the information obsolete? Until now, I thought it was an actual requirement to renounce other citizenships.
That is still the oath they make you take, but it has no legal consequences. You take it, eat the brownies that the VFW baked for your naturalization ceremony, and happily keep both passports.
http://www.immihelp.com/citizenship/dual-citizenship-recogni...