My DH and I sound very similar to you, except the other way around (I'm the saver and the one who doesn't like overspending, and he is the generous one). We had very different upbringings too.
Looks like I'm going against the grain here by saying it totally CAN work (we've been together almost 6 years). It just needs some clear communication, rules, and understanding of the other person's attitudes.
Take mortgage and bills out of it for the moment (because different couples will split things differently according to their income (we split ours 50:50 because we have similar incomes)).
Everything else that is joint stuff - groceries, eating out, clothes for the children, outings, subscriptions, cleaners, homewares, gifts for other people, etc etc - that ALL just gets paid with the same credit card and then split 50:50 when the monthly bill comes. The key thing is that we have a threshold for purchases - ours is £50 but you can agree a different amount - if the item is under this then we don't need to ask the other person. If over this then we need to discuss. And of course things do come up which still need a conversation (like how much money to put in our friend's wedding card or whether this gift for our daughter's nursery friend's birthday is too expensive or how much we're willing to pay for the garden to be done up) - but generally it's a quick conversation / a bit of research, and we come to a compromise.
AFTER all that joint stuff is taken care of, then the rest of our money is our own. The reason we don't share this is that we have very different attitudes to saving vs investing. I'm a saver and I need a safety net always, while he is a spender and likes trying out risky ventures and investments. So this way each of us feel like we can do our own thing. Obviously if we ever need each other's money for whatever reason then we'll give/lend it no problem, but there's an understanding that we each have different ideas about saving and spending.