We have two joint checking accounts. DH technically has access to both but only uses one. The one his ATM card is linked to has our gas / grocery / etc. money in it and I watch the balance and let him know when it's low and that there's nothing more to spend from it. The other, which is technically a joint account but for which he doesn't have an ATM card, holds the money for the major bills, which of course means there's money sitting in that account that's already been allocated much of the time. I do it that way because he also has that mentality that if the account has money in it, that money can be spent, and if we only had one account, it could very well be disastrous.
This system works pretty well for us (as long as I closely watch the balance in the account he uses...he tends to not do that and has been known to overdraw). I manage all our finances, pay all the bills, and do all the other day-to-day financial grunt work, and oftentimes I wish he wanted to be more involved in the nitty gritty of it all, but we've come a long way in terms of managing our money. I've learned both our strengths and our weaknesses and used that to our advantage to create a workable (not perfect or ideal, but workable) system for us. For me, a big part of that system is just making sure that I stay on top of things so that I can say to him on any given day, you have X amount in your account, or I can say, we don't have any more to spend this week. He never questions me on that, though, and trusts that I am keeping the budget in check. Our best months are the months when I stay really on top of things; our worst months are the ones I get behind.
If you're willing to take on the stress of the day to day budget and really get on top of it, that's what I would suggest doing. Figure out how much money is left in the categories he spends and tell him EVERY DAY. In months that are tight I do this with DH and it annoys him to some extent, I know, but it also keeps our spending in check, which is critical.
Your DH HAS to get on board to some level. It may not be the level you'd prefer, but I think it sounds pretty reasonable from all the responses on this thread that it has to be at whatever level you can make it work (and then you can aim to improve from there). Yes, it may mean more effort on your part than may seem "fair" at times, but I always look at fairness as an across the board thing. I may do more than my "fair" of handling the budgeting stress, but he does more than his "fair" share in other areas, so overall it balances out, and that overall balance is what makes our marriage...and finances...and everything else...work.