If you catch them stealing from your purse... how do you handle that - just ask them to stop?
You likley GROUND them or take thier car keys away or some such... Same idea with H... I know you can't ground him. but you CAN make his life unpleasant... the best consequence is additional responsability - stop washing his clothes, cooking his meals, and doing anything else for him... leave it go to crap so he has to put more time into it
Otherwise he's just using you and eventually you will get so miserable you will be physically ill
ASKING someone to stop cheating does NOT WORK... its an addiction. You can't expect an addict to stop using simply because you ask him to stop... they will just nod and do it behind your back until you catch them again.