To be completely straightforward, your boyfriend is acting like a coward. He says he doesn't want to make things hard for his girlfriend... ok... you know what's really really hard? Finding out you've been deceived in an ongoing fashion by someone you love.
This is deeply unfair to her on several levels. Let's take just one -- std risk. Right now she has every reason to believe her risk is low to non-existent because she believes she and her boyfriend are monogamous. However she is wrong about that. She should get the chance to accurately evaluate the level of risk she is taking on so she can decide what's right for her.
I'm not big on ultimatums but in this case I would issue one to your boyfriend. It's not fair to you and your husband to expect you to be involved in this demeaning and dangerous duplicity. This isn't some situation where he had no choice but to go behind his cold and cruel wife's back in order to maintain contact with his children... he's just doing the wrong thing because it's easier. If he's willing to do that, what might he be lying to the two of you about?
He has to come clean to his gf.
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.