Thank you for sharing your experience. It seems your partner isn't in denial about his problems with alcohol. However, you will have to help him realize that if he quits drinking it will NOT be as a favour to you BUT as the best possible thing that he could do for himself. As far as I know, resentment never helped anyone in recovery.
You know best what this relationship means to you and if it's worth holding on to. It is obvious that there are trust issues which need to be resolved. My sixth sense tells me that getting alcohol out the of the picture will help to a great extent.
Wishing you all the best.