trans | Transgender vs Bigender?

After another long long conversation with a friend, she got my head thinking... being intersexed, she said, only applies to physicality and that she thinks that because I identify as a mix of both binary genders, I should be transgender despite the fact that I identify as what I would call "bi-gendered" or "intergendered" and had been using the word "intersexed" to describe not only my physical sex but my internal gender. She said that it was a misnomer and that transgender better describes it. I don't necessarily agree, but I thought I'd pose the question to a broader and more experienced group of folks... what do you all think?