“He has a history of alcohol issues, he has known to black out and have no recollection. Both his parents are functioning alcoholics and whilst he doesn’t drink regularly, it’s clear he has an unhealthy binge drinking issue.”
He is an alcoholic. Fiddle with the words if it makes you feel comfortable - call it “binge drinking” or “problematic drinking” if that makes YOU feel more comfortable - but the actions / facts don’t change just because you change the words.
AA don’t define an alcoholic by how much they drink, how often, what they drink or when.
They define it by the impact it has on the people closest to them.
You have someone who has zero control and blacks out. Currently it’s once a month. Know that it is a progressive disease.
Him shagging someone else when drunk has had a HUGE impact on you - he is not even a functioning alcoholic because he is unable to function appropriately in a monogamous relationship. He will lose work days, his mental and physical health will continue to deteriorate.
Do not try to fix this man. Do not hitch your life, money, hopes and dreams to him.
Alcoholics are liars. They lie to themselves and others about everything.
I wonder why you are so in denial about his behavior. Why is this acceptable to you? What was your upbringing like that this is good enough for you?
You can do better. You don’t deserve the life of the alcoholic wife / partner.
Look up Al Anon online resources - it’s for partners of alcoholics.