The question you / he haven't answered OP is WHY he needs to keep track of the 'actual' balance of your bank account, at every moment.
What does he do with this information? How does it help him (other than feeding a mental fixation, which is actually a burden)?
If you were living very close to your overdraft limit and a small transaction could push you over the edge, or, if you were a crazed spendthrift, prone to making major and unaffordable purchases on a whim, I could see the point. But you've said that's not the case.
Here's a suggestion - agree all major purchases, or those that fall outside 'standard and expected' categories in advance (your definition will depend on your means, for us it's anything other than groceries, insurance - or anything else that is expected, over about £100).
Check regular bills and expenses periodically, maybe every six months or a year, so you can see if you're spending more on fuel, insurance and groceries etc. and can decide what to do about it.
That way - given that you're not on the edge of solvency - there really cannot be any unpleasant surprises, so no need to worry about the difference between your balance now and in a few days time. Simple!
That's how I budget, in three categories:
- dd into household account, checked and adjusted annually.
- budget for personal spending, checked and adjusted annually.
- Amount budgeted for 'major purchases', discussed and agreed individually.
Obviously, if you're running one joint account, the first two would be combined. The essential thing is that you've budgeted realistically, and are aware enough of your budget not to overspend massively. Voila!
The only reason I check totals monthly is because we are living very close to our overdraft limit, which is a cashflow issue, not a budgeting one.
It's good budgeting that keeps costs down, not observing cash flow passively, as your DH seems to be doing.