hoping for better times to come

[pearlharbr]

Do not misunderstand Maple, asking him about OW will produce only one of two responses: no or she's just a friend. Remember that ALL CHEATERS LIE.

IMO, you cannot work on your R with another person involved. It just won't get you anywhere because H will be telling you what you want to hear and telling her what she wants to hear to continue the cake eating as long as possible. You cannot rebuild a M on a foundation of lies.

My BF lied to my face on a daily basis, even when I had proof showing when and where he was meeting OW.

This is why I tell you to trust your gut. If you think there is OW either get some proof or move forward assuming there is one. This would entail setting a boundary with H that you will not be in an open marriage and if he is serious about recommitting to you then he will have no problem with implementing a transparency plan.