If your husband has forgiven the cheating, do you think it's helpful for you to hold a grudge?
You don't have to like your husband's girlfriend, you don't have to spend time with her. But if you're going to expect your husband to approve of your boyfriend staying a night in your house, then it seems only right that he should have the same privilege. I'm big on "What's good for the goose is good for the gander," provided the goose and gander actually want the same thing.
As for how to bring it up, I think you're right that just taking alcohol and reactive emotions out of the picture will help a lot. The exact wording isn't important as long as you're being supportive and open-minded. Remember to let him speak his feelings without judgement. But also, be prepared that he may not agree to your request, especially if you're not willing to return the favour. In other words, don't get too attached to that outcome because you could end up mad if he says no, and then the discussion may spiral downward from there.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker