Wow, what an entitled ass. He has your permission to work with you on finding a third partner, and yet he cheats -- in an ongoing, long-term way, it sounds like -- and then expects you to just accept that you've been living a lie and tries to give you no choice in who to share your heart and your body with. That's just sick. You shouldn't stand for it, no two ways about it.
If nothing else, there's this -- by cheating, he opened you up to STI risk that you knew nothing about. In an open, honest relationship, you could have assessed what you were comfortable with in light of who else she might be with her or might have been with in the past, what her testing status is, etc. Instead, he took your control over your own health out of your hands without your knowledge. Again... just sick.
Maybe pack a few bags and stay with a relative or friend for a minimum of a week, while you decide whether there's anything to salvage here, or whether it's time for you to move on.
The major players. Me, 30ish bi female. Gia, girlfriend of 4+ years. Clay, boyfriend/dom. Davis, ex/friend/"it's complicated." Eddie, roommate & fwb.
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy and Nikki, Clay's partners. Liam, Eddie's husband.