Interestingly, Eric is exactly the same way as your husband. Gia doesn't so
much forbid him to do anything or see anyone, she just keeps her more emotionally-attuned eye out for when he's about to get himself into trouble (i.e., this person is a bucket of drama, this person clearly wants a type of relationship you can't give, etc.) and strongly suggests that he make the smart decision since it's likely to affect them both.
If he some day suddenly had a change of heart and actually *wanted* to be emotionally entangled with someone else I think she would do her best to ascertain whether it was genuine or whether he was confused, then ask him to go slow if it was real. But it would be a big adjustment and possibly a bit of a shock to her system, since he's been so momoamorous for so long, and I do think she would fear that he would not, in fact, have "infinite love" to share since he's never shown any signs of being polyamorous before, and that he might pull away from her.
It would be a scary time and I think she would let him go for it, on the chance that his ability to love really had expanded, but would keep a very close watch on things and have a long, hard talk with him if it did seem like he was pulling away from her emotionally. I hate to think that she would throw a veto, but it might well come down to that -- they have their kid to consider.
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.