I'm a native speaker of New Zealand English (similar to British English) and I can't think of an occasion when I'd say or expect to read 'intermixed'. I would always use mix or mixed. If I read intermixed, I'd assume it was an adjective used to emphasise an unusual mixing (eg of people from different culture).

Intermix is a bit tautological because mix alone already means to combine ingredients. I would advise that you don't use it. There could be a situation where it has a special technical definition, such as to mix while leaving the original ingredients whole, but I can't think of any examples where mix isn't sufficient.

I think, words "intermix" can only be used as a verb. The words "mix" can be used as a noun and a verb.