He's a dick. And a dick that has made it clear he doesn't want you cramping his style on a night out. Nice.
Soooo...
you're saving (mostly you)
when you suggest doing something together the answer is no, no money to be spent. you don't get to have fun.
but when there's a chance for him to go out and have fun - oooh yes please. The budget can definitely stretch to that!
You could come too, to this. For once you could BOTH get a rare night out.
But no. Not only is he happy to treat himself, he goes one step further and wants you specifically not to get a chance to go out. No. You'd cramp my style. Not only do I want to make an exception to the budgeting for MY fun, I specifically want to prevent YOU from sharing it.
In what possible world is that not a completely arsehole way to be?
People saying oooh you're not joined at the hip are totally missing the point. If they were both out all the time doing this and that with loads of joint stuff happening, fine. Time apart socialising with separate friends is healthy and good. But they aren't. Fun nights out are thin on the ground full stop, and he's happy to police that. So a night comes along which you could both go to, BOTH of you having few opportunities recently - and he's not just keen to take the limited fun cash pot and spend it on himself, he's determined that you don't share it, and sit home alone for yet another night in. Selfish shit.
It obviously raises a Q about who he wants to talk to and what he wants to do that he doesn't want you to see. But that's almost by the by. The problem here is that this person is not your friend. He may be your partner, but he isn't your friend. He sees you not as part of his circle of friends, but as something slightly apart, something he wants to keep at arms length when it suits.
On my own personal twat-ometer, this one scores particularly high. 
I have NEVER come across a bloke who thinks of and treats their partner like this who isn't also a massive bellend. You are 'er indoors. Not an equal. He sounds quite fundamentally shitty and your FT conversation rather confirms that.
My answer to all this would be a broad grin and 'Great! See you there :) ' Then I'd go, have a fine time talking to other people, letting him get on with it and spending what I damn well liked. Then when he UNDOUBTEDLY had a face like a slapped arse the next day and started making comments about saving and how awful I had been to presume that I should also go out and have some fun, I'd just shrug and say 'no matter, do you know I'm not so sure anymore about putting in 90% of the deposit on a house to live with a bellend anyway. So I might just start relaxing MY purse strings a bit and making a few more friends, seeing as you're so desperate to make sure I don't cramp your style by being a part of your social life. Good luck with the debt repayments, twatty!'