As for the term "bi-monogamous" I have also not heard of it, so I wouldn't presume to give it a hard-and-fast definition.
If I read it, depending on context, I would probably think it refers to poly people who want to have one male partner and one female partner. No information is implied whether they would accept a transsexual partner, a gender-neutral partner, or whatever else people can come up with to gender-identify.
I completely agree with AT that it's not monogamy at all. Monogamy is one partner, period. Two is not equal to one.
I can't understand why someone would have such a policy, but there are many aspects of some people that I can't understand. I mean, if you like men and you like women, and you're capable of polyamory, then why would you deliberately turn down someone to whom you're attracted, just because you already have one of that gender? It's like ordering dinner at a restaurant... pick your potato: do you want fries or mashed? You can have both, but we'll have to charge you extra.
Gralson: my husband (works out of town).
Auto: my girlfriend (lives with her husband Zoffee).
The most dangerous phrase in the English language is "we've always done it this way."