I've told my girl many times. I am not Chinese. And I will never be. Even though I wish to learn Chinese language, culture and customs.
We have also had many misunderstandings. But we talk it out. Find out what are the cultural differences or why has there been misunderstanding. Or why is there a problem in the first place...
She and I are beginning to understand that there are a lot of things the opposite in our cultures, in the ways we speak and express our selves... So there are going to lots of things that feel rude, or wrong, or evil, sad etc... But then we just have to ask, talk it out, figure out whats going on. "is this what you meant?"... Usually its me doing most of the work. But still its together...
I've also asked her if she wanted me to be Chinese. She has always said no. That no Chinese man could be as nice as I am, or as caring, etc etc...
You need to let her know what is acceptable. What is not. My girl has tried to be jealous, sad, many things... But some things are not acceptable. She just has/had to learn to trust me. And I always tell her if I feel that something is not acceptable...
Especially jealousness was a big problem at the start. She always felt and thought that I could leave her any day. But the longer we know, the more she knows me. The more she trusts, the better she understands.