Apologize profusely. More than anything else. It may take a thousand apologies, but eventually it'll sink in.
Do not blame him or the marriage for your choice to have an affair.
Read the thread pinned to the top of the Wayward forum about what every WS needs to know.
Reconciliation typically takes a few years. Yes, you read that correctly. Years.
For most people, the betrayal of infidelity is a profound shock and a severe emotional and psychological trauma. Your BH is likely lost in a world of unbearable pain and confusion. It took me about 10 months just to recover from the shock and several years to heal.
If reconciliation is your goal, you're going to need more patience and resilience than you ever thought possible.
Do your absolute best to encourage him to stop drinking. It will numb the pain in the short term while prolonging the healing process.
He needs space and time to pull himself together. It's not easy to do. It's the hardest thing I've ever had to do.
As gently as you can, draw your own boundaries when it comes to verbal abuse. Many of the lashings I gave my WW (now ex-wife) are truly regrettable. I'd never felt such rage and hope to never feel it again.
Be patient. Apologize often, for specific things when possible. Be open and honest about everything no matter how hard it may be. Betrayed spouses become hypersensitive and hypervigalent, symptoms of PTSD. The slightest hint of dishonesty or obfuscation will be detected.
We have a "Healing Library" here at SI. You'll find it in the links tab. Scan through it and print out any articles you think might help him. Do not tell him about this site. Too often, unfortunately, couples both using SI turns out badly.
For some folks, infidelity is a deal-breaker. There's no other recourse. He might very well leave no matter how hard you try.
So now comes the really hard part. You have to let go of the outcome. Whether he chooses to stay and attempt reconciliation or leaves and divorces you is entirely beyond your control.
Your priority here is doing your best to dig deep within yourself and figure out why you chose infidelity to escape whatever issues you may have (we all have some). He'll want to understand them as well as he can (maybe).
Marriage counseling won't help this early out. In a couple of years, if reconciliation is going well, it could certainly help.