While neither I nor you can diagnose your girlfriend, it is possible to have schizophrenia/schizoaffective with DID.
A friend of mine from IP had both DID and schizoaffective disorder. With his DID he had two (at least) identities, but he was very self aware in that he knew when he wasn't himself. With his schizoaffective he heard the random voices, and I'm assuming had other symptoms, I'm not exactly sure.
I have schizoaffective disorder and have somewhat toyed with the idea of having DID (although I'm 90% sure I don't have it). Any questions about my friend or myself and I will try to answer if I know.