Sounds to me like it's a V. Your husband and your girlfriend are tied much more intimately to you than to each other, even though all three of you share sexual relations.
The only suggestion I'd make is to not expect all sex play to involve all three of you. You and her without him and you and him without her would be reflective of the emotional ties that already exist and can complement the threesome experiences well. If he and she don't get together without you, that's OK, as there's nothing to be gained from forcing things to meet artificial expectations.
Having a V doesn't preclude the three of you also acting like a triad at times. When it comes down to it, the members of a V have to relate to two other people, the same as in a triad. So loving and caring for the other end of a V isn't unusual in the slightest--and it's a very, very good thing.