Have you all talked in trio already? All 3 in the room and BF state to husband that he's not looking to break you up?
Past that, most of the stuff is on your DH. That he thinks you are BF are more of a couple -- yes. You are a couple. And? It is one dyad in the larger polymath
of this polyship. So?
It is not on you to solve his lonely when you go out with BF. You can say "I am sorry you are lonely" but the answer is you NOT going out. Because you have to do your own time management and share with DH and BF fairly.
You are responsible for providing support and nurture and a listening ear. Not do work FOR him in relationships. Everyone carries their own baggage.
DH has to find ways to keep himself busy so he is not lonely. If he wants to meet women -- go! Look at online profiles, join an interest group for his hobbies so he meets people with same interests -- mingle out there!
He is responsible for his own stuff. Is he wanting you to be his wingman or something?