Is it possible to feel like both a masculine woman and a feminine man?

Like, I feel like I have a bit of both in me. Most androgynous people have the feeling of having a feminine woman and a masculine man in them, but I feel like I'm a mix of femme man and butch woman in me. Is this possible? I mean, I know I'm physically female, but I've never felt that way. I've always known I wasn't inwardly a girl, I just never was quite able to put my finger on what I actually was.