Hi trueno92, thanks for posting the pics. Your Chinese bike is very similar to my Downtube Mini, so I'm sure I won't be able to fold with basket attached either.
I may go for a regular lift-off non-folding basket to save the hassle of having to strap/re-strap on the folding one. This basket looks like it might work:
http://www.amazon.com/Wald-Standard-.../dp/B000AO3H2Y