Regardless of whether he is or is not cheating/drinking, relationships need trust in order to prosper. If he is giving you reasons to not trust him, I think you should communicate how you feel in detail and why it is important that you both are full frontal about these things. If you feel as though things can't change and you can't leave him to his own devices, I would suggest that this relationship may not last in the long-term. Moreso, that the relationship may not be healthy either.