If you have any strong support at home like a family member who DOES realize his affair is NOT solving anything and that it IS hurting you then have them THERE.
The idea is to confront him... not to have a secret little chat somewhere and solve it in private.
You make this a family meeting... do NOT warn him.
He shows up and there's twelve people in the room and he has to sit and listen to them all tell him he's failing as a husband, but that he has a rare opportunity to repair his marriage since you are willing to explore that.
He is told that he accepts that, or he LEAVES with no visit.
The thing is, there is no leverage on your part or consequences to him cheating. He cheats, and it causes HIM NO INCONVENIENCE.
This meeting is to cause him inconvenience. He will be told his infidelity will be exposed further to more people and that no one will talk to him etc.
If he realizes he is not just losing YOU, but his entire FAMILY and that he has a choice between
Public Humiliation Public Reconcilliation
He should choose the latter.
Right now we need to build up serious consequences for him to choose to continue infidelity.
And he will likley try to DENY it, do NOT have anyone in that room who isn't supporting of you or this intervention.