It actually sounds like he wants to avoid the term because of his own jealousies. If he can keep you around in spite of his cheating, but not open up the relationship (he may be assuming you will want the freedom to date and see other men without him) for the both of you, then why would he need to?
I would say start getting your needs met in this relationship. If you are curious about a mono/poly combination relationship (where you are mono since you stated this is your orientation and he is poly and you are comfortable with that) then he should give you a chance to communicate with him and he should communicate with you how he feels about that. It isn't fair for him to stonewall you and refuse to talk about it while he basically has an affair in front of your face.
A healthy relationship will not spring up out of sweeping things under the rug and pretending like it isn't happening. Depending on how you feel about things, there are a few ways you might call him into account for this.
"I do not feel comfortable with you seeing Molly if we cannot discuss polyamory as a couple and come to an agreement we can both be happy with. Your relationship with her has gone beyond just sex and I am not comfortable with that until we can hash it out in an organized manner and set down some boundaries and make sure we see eye to eye on everything. I am willing to consider being in a polyamorous relationship with you, but I am not willing to let this "thing" with her continue until you can be honest with me and address my needs for communication in regards to it."
"As your girlfriend, I need a certain level of communication with you. Even if polyamory is not something you end up wanting for yourself or for us, I really need to discuss it with you to make sure we are on the same page. I want us both to make any decisions together, but I don't want to keep avoiding this discussion. Your recent indiscretion has caused me to question the structure and nature of our relationship and this is a discussion that I need to have even if you don't want to have it. Please give me this respect as your partner."
Those are kind of long winded, but you can probably piece together your own thing out of some of the elements of those. I can't imagine staying in a relationship where my partner(s) refused to talk to me about any subject. Open and clear communication is one of the single most important aspects of a healthy relationship. He has not been giving you that, and has been having his fun on the side while parrying away your attempts to treat this in a mature and open-minded fashion.