As others have commented, not only should she ask 'Do I get a hall pass as well?’ she should also clarify that he’s willing to say at home with the kids, when it’s her turn to flash the hall pass. Ie: she gets reciprocal weekends to herself and whoever she might want to cufk.
PS: I have no idea if he’s already cheated. I have an old friend who’s wife wanted to open the relationship. He said they had a lot of conversations before they opened, but they’re still married. He is the last guy in our friend group who I would’ve thought would be in an open relationship.