You can wring the alcohol out of an asshat and all you have left is a sober asshat.
Character issues are character issues. Trust is an essential part of a relationship and I would be very wary about a cheater.
My husband cheated and I gave him another chance after he groveled and begged. It was a mistake as he cheated again... that tore it and leaving him was the smartest thing I ever did! My kids are grateful today as he is still a loser!
Can your husband change his character? Yes... but only through an honest, authentic program and sounds like he is a looooong way from that right now. And if he does become a person of integrity, honor and trustworthy it will take time and you will know that he is a different person.
Time is your friend... it will reveal much. Keep him distant and watch his actions...