To me, if your potential GF is going to be with her BF only, then it is a "closed polyship " or a "polyfidelitious" arrangement of 4 people.
If she is going to be dating others, it is an "open polyship" to me because even though you and husband are closed to each other and the GF, the GF herself is not closed to just you two or you two and her BF. She's dating others too. So the polyship as a whole is not closed. If you wanted to use "partially closed" or "partially open" that could also work since (1 partner open) is different than (all 4 partners open) to dating more and maybe you want to make that distinction.
Maybe this article
helps you with vocab for relationship models?
Ultimately what you want to use for vocab is up to you guys. But I get that being able to say "something like an X" is helpful shorthand.