Most people I know don't go to clubs till 4.am with colleagues. They might go for a meal or drinks and some of the young singles might go on somewhere at the end of the evening but most people will be heading home.
He needs to be thinking about why he thinks it's OK to go on all night piss ups with work while his wife is looking after his baby, especially as he clearly has no self control.
He has behaved very badly, shamed himself, disrespected and hurt you, potentially destroyed his child's family. Offering to leave work and swearing on his child's life are pathetic, self dramatising cop outs. He needs to understand how badly he's behaved, why he allowed himself to do it and how he plans to address the lack of self control, self entitlement and disregard for his marriage, his wife and his child that enabled him to do it.
If he can explain and address that to your satisfaction, it's possible your relationship can survive.