Regarding the "American side", it sounds as if the US firm will issue you a 1099-MISC for nonemployee compensation - this will clearly be subject to self-employment tax.
The "Chinese side" is indeed trickier, made more so by your referring to it as the US company's "rep office". What do you mean by "rep office"? - is it simply that, an office of the US company opened in China with no separate legal personality (not a Chinese corporation, etc), or is it a Chinese corporate subsidiary of the US company? It makes a big difference:
--if the rep office is merely an office/branch of the US company with no separate legal personality of its own, then your pay from it is just like pay from the US company (even though paid in yuan/RMB from a Chinese bank acct), and should probably therefore be considered additional self-employment income since the US company is already treating you as self-employed (indeed, the Chinese-paid income should in this case also be reported on the 1099-MISC)
--if the Chinese "rep office" is a separate Chinese subsidiary company, then you need to determine your work relationship to that Chinese company based on US tax rules, i.e., if you are an employee (under US legal/tax principles) then it's wages (no US social security or SE tax), but if you're self-employed with respect to the Chinese company that would just be more income subject to US SE Tax. It's admittedly a bit strange to be a consultant to a US parent co, and an employee of its foreign subsidiary. Usually a US company doing a "split" like this would make you an employee all-around.
Thus, you need to better understand what that "rep office" really is.
Good luck.
Les Edelman
www.edelmantax.com
Circular 230 Disclosure: as stated in prior posting