I personally don't think that's actually crazy. He lied to you. When someone lies to you and you think they may be you generally go look for the facts (the passport).
That seems logical to me. But, as with alcoholism, now you know. He is lying to you. The only question is, what do you do with that information?
That really is entirely up to you. Sadly the choices are to accept this the way it is or not. He doesn't seem to want to quit drinking at this point.
I'm so sorry this is happening Asy. I know it causes you a lot of pain.