Sorry for the late report back... it took a while to arrange things.
My husband invited his girlfriend over just so we could meet, and it was surprisingly not awkward at all! I'd been bracing myself for some true weirdness. It turns out that she's very nice, and seems truly open to a non-traditional relationship. She said that she'd been nervous about meeting because she thought that I
would be possessive, or that there would be some sort of hostile competition between us. Phew, all that worry for nothing.
Now onto the next topic of worry... dividing our time!