Oh dear. I have actually lived through this almost exact scenario, obviously different words said, but the vibe very much the same. It happened several times with several different women. I don't want to panic you, but for me it didn't end well. It was exactly what my gut was telling me.
Of course he will deny, deny, deny. For me, I went through his phone when he was passed out drunk, and all the evidence was there. I would urge you to do the same. Turned out he was sleeping with my best friend too.
Suffice to say, I left. We also had young kids at the time, it was not easy.
I'm married now to a man who has never been this disrespectful. If he is up to no good, don't waste your best years on him.
But first and foremost, you need to know what you're dealing with, and I would go to any lengths to find that out : go through his texts, whatsapps, e-mails, bank accounts etc. Don't sleepwalk through this.
If there are any nights out in future, I'd pretend to drink, but actually order soft drinks. Order yourself a tonic water and tell him it's a G & T. Your observations when they are drunk and you're not will be telling. I was often drunk when these things happened, and it was always hard to recall exactly what had been said, which makes you doubt yourself.