My perspective is a bit different: I'd examine the stated intent, then check on follow through before branding someone a liar. Should I ever find myself in this man's situatupion, and I felt the need to cheat, everyone would know my intent. I would so totally own what I'm doing.
To the wife "I'm not sharing any aspect or information of my life in this regard. You show no interest in it, so make of that what you will." And follow through. Refuse to discuss it with her. She is not entitled to know.
To my prospective outsidevrelationships: "this is my stuation. I will not end my marriage for x reason. I have these boundaries in my marriage that I think will impinge upon our relationship in this manner. Here is what I can offer, and what I'm hoping for." And then follow through...
If I stick to my intent with my actions, at least I've mantained my personal integrity with myself, even if others might disapprove. And yes, it's not poly. Where is the multiple loves?
You'll should do what is correct for yourself and actively decide what works for your relationship. It doesn't sound like your BF is in a space where he can do the same, unfortunately.