And so, since you know this, what are you going to do?
This is your life we're talking about, your happiness and your future. We only get one go round. Do you really want to take such a big chance that he's going to stop drinking and become a 'productive member of society'? Because chances are he won't. And why should he when you're there to facilitate his alcoholism & cocklodging?
And here's the other thing. His constant accusations of you lying. Has it occurred to you that he's doing it, not because he truly believes it, but only to keep you 'proving yourself' to him? He accuses you of not loving him or cheating so you bend over backwards to prove how important he is to you. He accuses you of 'being distant' or 'in a bad mood' and bam! You stop complaining about his ways and go silent in order to 'disprove' him. This tactic is as old as time.
Stop and think how much more peaceful and easier your life would be without him. Calmer home, more money, less stress. Why wouldn't you choose that? Why live in unhappiness for the sake of being 'coupled up'? It makes no sense. And remember, too, that you'll never meet Mr Right when you're all entangled with Mr Wrong.
So in answer to your question "Does this ever get better?" no, it doesn't. And it usually always gets worse.
If you feel like saying, what is your living arrangement? Your house, his house, renting together or separately? Don't let some sort of financial entanglement with him stop you from extricating yourself. Sometimes it's simple to break away, sometimes it takes a bit of time and finagling. But it's always worth it.
And please, please double up on your contraception. You don't want any unfortunate accidents to occur during this period of reflection.