An all cash system certainly has some great strengths to it, we did have cash envelopes as a budget over a decade ago, I think it worked ok despite our cheating. It does take buy-in as Clutchy noticed, freeze the debit and credit cards in ice or whatever it takes to make the two of you stick to whatever system you choose. Remember that habits die HARD. Just because you have to take draconian measures to start with doesn't mean you have character flaws of similar proportions, and it doesn't mean you will need to live like that forever. It often just means you need to take a few months to build new habits, and the draconian measures can be helpful. Best advice I can give is to actually think and discuss your routines and purchases together, and come to some agreement about what they should be. Then figure out what it will take to produce that. From your descriptions it certainly sounds like a budget is needed, and it also sounds like you need to keep track of every dime for a while and see how much you are losing to fast food, convenience stores, amazon, target, etc. Just putting a number on it every month and shaming yourselves by reviewing it together can make a huge difference.
Like c said I don't like to use much cash because I don't keep track of it as well, but a good system of keeping track of cash purchases would take care of that.