During his affair, my husband referred to her as his "girlfriend" and "partner" - why would he do that?

He called her those names because he respected, valued and loved this woman enough to refer to her as something other than the broad he was banging on the side. The very fact that he referred to her as such must really hurt if you've posted the question more than once. I'd be careful in your relationship with the cad...if he thought this highly of her perhaps they may have a future planned without you in it. Apparently your friends understand this since they've allowed her over for dinner.