"I don't know what the terms of the types of relationships are."
There are no standard sets of terms, per se, it's all what the individuals involved work out as being best for them and their relationships. This is a great website for understanding that perspective, as well as for good advice on jealousy: www.morethantwo.com
That said, there do seem to be several general patterns that people commonly fall into in your sort of situation:
- The unicorn hunters. The preexisting couple (you and your husband in this case) both start dating the new partner, and may expect that person to not date anyone else, move in with them, be into them both equally, etc. Nothing about this ever seems to go well, as it's just too emotionally volatile (not only are new relationships forming, which may not be given all the space they need, but the preexisting relationship is changing, which can be very threatening to the preexisting couple) and unbalanced in terms of power (notably, the new partner being burdened with impossible expectations).
- The serendipitous triad. Much rarer, this looks like the unicorn hunters model except that its development is not an expectation that anyone has going in, rather it's a dynamic that begins to naturally take shape, and it usually develops much more slowly. If things are lopsided (ex. the new partner forms a much stronger bond with one partner than the other) that's ok, and all members generally maintain their right to date outside the triad (although a poly-fidelitous or closed version of this type of relationship is not strictly impossible).
- The heirarchical vee. A vee is a relationship in which one person (the "hinge", in this case your husband) has two partners (the "wings", in this case you and his girlfriend) who do not have a relationship with each other (though they may be friends). In the heirarchical vee, the preexisting couple's relationship is given priority in terms of time and investment. This may simply be a function of necessity, due to commitments such as children, it may be a natural expression of where each relationship is at (the older relationship being more serious, the newer relationship being more casual), or it may be a conscious choice to position one partner as "primary" and another partner as "secondary". This model may have accompanying rules, whether implicit or explicit, that govern the functioning of the newer relationship. Broadly speaking, these rules can work when they are about practical things like time management, and/or when they exist for the purpose of maintaining the integrity of the preexisting relationship (ex. "Only one overnight with the newer partner per week, because the hinge is needed at home for emotional support, help with the house, etc.), and tend to fail when they are about impossible to control things like feelings, and/or when they exist for the purpose of stunting the development of the newer relationship (ex. "Don't say "I love you" to the newer partner, or have PIV intercourse, or introduce her to your mom, because that would make that relationship too real, which is scary").
- The egalitarian vee. Similar to the heirarchical vee, expect that the two hinge-wing relationships are given equal time, priority, and investment. The newer partner may move in to a home shared by the preexisting couple in this model. The heirarchical vee may in some cases develop into the egalitarian vee over time, if allowed the space to do so, or it can be chosen at the outset of the newer relationship's formation. If an egalitarian vee is chosen as a relationship model without the full consent and acceptance of the preexisting wing, or when the relationship between the hinge and the newer wing is tumultuous, it can be destabilizing for the relationship between the hinge and the preexisting wing. Works best when the two wings get along very well.
Well, this was fun to write, I hope it was helpful.
I may actually copy and paste this list into a thread in the general section for feedback.