Similar to what H said individuals who have bipolar disorder are at a higher risk to have alcohol/substance abuse. It is usually treatable, however, if the person is willing to recognize the problem and do the work. It can be a long road not only for addiction recovery but also finding the right meds to treat bipolar and keep it under control. It doesn't happen quickly.
The personal experience I can share is that I have bipolar II and I have two close friends who have bipolar I. All three of us are sober alcoholics. I have six months and my friends have 6 and 18 years. All three of us have to be careful to take the meds and follow-up with our doctors to keep the bipolar treated. It hasn't been easy for any of us, however we are all leading very different lives than before (for the better!).
Whether to stick with him is not something I can tell you, it depends on how you feel about it, how long you have been struggling with him, if he is willing to work towards recovery, etc. I wish there were a simpler answer to give you.
All my best, HopeOct31