Sit your partner down and explain to him that his behavior is totally unexceptable and if he wants a family he is going to have to change his ways.
Find a parenting course that you can go to together or if that is not an option separately.
Keep him on track , don't let your guard down with empty promises of change.
Put all your energy into fixing the unhappiness in your life.
HOWEVER, at the end of the day do not live with regret.
If the behavior doesn't change and you have looked at every avenue to correct it, have an exit plan that will not alienate your partner from you and your child as you are connected for decades to come.
Make him aware of this and at the end of the day he can't say he wasn't aware of your unhappiness with his unacceptable behaviour.
Good luck life is tough but have strength .