Every time I see this thread title, I think of people who simply have two lovers. There's nothing in it to indicate whether those involved are gay, straight, or bi. When I was involved with my wife and a girlfriend and nobody else, I was biamorous--and I'm strongly heterosexual.
When speaking of sexuality, relationship style is divorced. "Gay" doesn't indicate mono or poly, nor does "straight" or "bisexual." Those terms speak solely to sexual attraction. Likewise, "monogamous" and "polyamorous" don't speak to sexual orientation.
I'd say it's going to be extremely difficult to find a set of terms that would cover both, and "biamorous" on the face of it, speaks only to relationship style.
Furthermore, as there are bisexual folks who aren't necessarily poly, one can't automatically tie sexuality and relationship style together for bi folk. I know serial monogamists who are bi and bi folk who fuck around and don't engage in romantic relationships with most of their sex partners.
I'd love to hear a set of terms that could describe all of the permutations and I've no problem with accepting a different term to cover bisexuality. "Pansexual" has its problems--seems to imply attraction to all animal life forms--though I can certainly live with it.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.