I can't for the life of me, fathom why he needed to "make it up to her" wrt the the previous weekend... if he was just popping to see her because she was 'down', and you put a stop to it, why did he need to make anything up to her? Why does he owe her a night with him?
If I've felt crap, and asked a friend to come, and they've cancelled, they've never come/invited me over another time, just to 'make it up to me'.
It sounds (the making it up to her), as if he/she were viewing it as a date.
I have to say I disagree with a previous poster upthread, who said that they should back off, and then get together alone, when you're comfortable with it... surely their relationship needs to go back to what it was before - why should you ever be comfortable with a shift in the friendship, where he has this female friend over for the night, when you're out.
Has the female friend contacted you OP? Surely if she was a genuine friend then she would have realised how upset you were the other night (let alone the weekend before) and would have contacted you to offer her profuse apologies, and reassure you that it was just an innocent friendship, then maybe suggest that the two of you have a night out. That is what a true mutual friend should do.
I wouldn't agree to the ff coming over or socialising with the both of you tbh. Might sound nasty, but the conniving bitch female friend, should be doing damage limitation if she is genuine. It would be normal for a single female to go out with another woman, or group of women, not go to a married man's house when his wife is out for the night... how the heck is she going to find another man staying in with your DH though of course maybe the man is there
I would invite her out, on her own, with you. Stop all your DH's contact with her... I bet it won't work, it sounds as if they're already emotionally invested in each other... and your DH's attitude sounds very much like he's infatuated with her.