You need to have a life too, your partner sounds happy to swan off and leave you in charge. Doesn't sound very fair if you miss out on a wedding anniversary night out and he gets to go out the rest of the year. Has he ever sat in with the DCs of an evening while you've gone out? He's not a bachelor, he has responsibilities.
Getting to know other mums with children in the same age group can help. Have you looked into what's going on around your area? Playgroups, church hall or community centre mothers & toddlers, softplay, swimming/aqua groups? You must feel the four walls are closing in.
I don't know what age your DCs are but would your mum be willing to babysit in daytime if the older ones are out at pre-school or nursdery? Just to give you time to do something for yourself, shopping or better still, exercise or hair appointment?
Once you get to know other people, you can sort out babysitting amongst yourselves, if you know them well enough to think you can trust them, that is. Not much point organising a night out if you can't relax because you aren't confident about the babysitter. Needn't be for cash, just return the favour, keep a tally.
Obviously with 4 DCs of your own you would need to find someone who was up for the challenge so for now you'd probably have to restrict this arrangement to evenings while the youngest are already in bed and settled. I'd say, this frees you up to go out with your husband, but I'm not so sure you should do all the running around then make the arrangements to go out with a man who scuttles off leaving you alone.
If you have been unwell and your partner isn't pulling his weight, no wonder you feel fed up. I don't know anyone with 8 children, 4 is quite a lot imo, he doesn't seem to realise surely the more both parents need to work together? How often a week does he go out in the evening? Is he seeing mates round their place or propping up a bar somewhere? Quite a lot of money spent if he is Mr Sociable.
You mention problems already existing and on top of that you are now risking depression, if you don't already have it.