they did not ask my parents if I went back to china or not since i came to us. they asked them how many children they have, how many children i have, whole family picture (my own family picture) and my legal visa or status documents. but my father told me even though vo asked my docu, she did not look at carefully. just one or two seconds. I did the excenllent job I think. I prepared the docu. by myself.
1) cpoies of your both SSN cards
2) inviting letters from your both companies
3) Financial support docu. including the last two months pay checks and bank statements, I-134 forms
4) legal status or visa from your both and copies of your both passports
they did not take a look in most time. just in case, if they ask your parents about these.
one more thing: tell them the truth, do not lie!!!!
good luck