wow...you are in a tight spot there....
Did your parents get to know Emily? Maybe getting them to know Emily might shake their view a little.
My mom use to think that all Cambodians are bad and she tells me to stay away from them, but nevertheless i didn't, in fact most of my friends are. Anways, many a times i bought my cambodian friends home to hang out, and i would talk a lot of good things about them once they leave, like how they got straight A's and do volunteer work and even helping me with home work, eventually she began to see things differently and accepts me hanging out with them.
(because of where i live, there are a lot of asian "thugs" and most of them are cabodians, thats why my mom thinks ill of them)
I hope that helped a little.
best of luck to you