Marriage advice

So drinking had kind of always been an issue for me in our marriage. My husband hates when I drink bc I have a low tolerance and end up getting out of control. I had promised him that I wasn't going to do it again (this only happens about once a year). I broke our promise last night and drank and lied to him and he found out. I feel so bad that I betrayed him and made him not trust me. How can I prove to him that I am done drinking once and for all. How do I show him he can trust me again. Please help me here. I want to save my marriage but he is saying that was the final straw and he may leave me.