Thanks for writing to Just Answer.
If you are considering continuing this relationship, which it sounds like you are, the most important thing for you to do is to first go to Al-anon (the group for people involved with alcoholics).
To try to be in a relationship with someone whose life is in chaos due to alcohol without the support of al-anon is to set yourself up for a life of heartache. If your bf is drinking enough to be blacking out, he is an alcoholic. To try to persuade yourself that he isn't is a mistake.
The most important thing to know going forward is that "What you see now is what you get". Do not go into this relationship thinking that your love and devotion will convince him to stop drinking. Most problem drinkers have to hit bottom and come to their own realization that they are out of control....when confronted by others, they will make promises they can't keep, make futile attempts to control how much they drink, etc.
Do you get enough out of this relationship to put up with further episodes like the one your described? Does he make you feel loved, respected, and do you know he will always "have your back"?
It is possible to love someone, but not be able to be in a relationship with that person. Your family and friends who love you think this is not healthy for you. If you saw your best friend getting re-involved with an ex who was an alcoholic, cheated, and lied, what would you say to her? When she said to you "but I love him" what would you say to your best friend?
Quitting drinking is not enough. There is being sober, and then there is being in recovery. All the good intentions in the world will not keep an alcoholic away from drinking forever...that's why people have found the 12-step programs so helpful. Unless there is something healthy to take the place of the alcohol, when the person is under stress, they will go back to drinking...it is the nature of the disease, not a moral failing.
Know that if you continue in this relationship you will need a lot of support. Alcoholics are not known for being dependable when they are still in their disease. No matter what you decide, it would be good for you to check out al-anon. If we are drawn to alcoholics, it often means we have some co-dependency issues that make them so appealing. Al-anon is a lifesaver for people in your position.