Generally all cash works best when you are trying to save. It does not allow for you to go "over" at ALL and there are no exceptions. If there isn't any left, then you can't spend it. It is far easier to "go over" when using a card--because, that extra dollar just doesn't matter in the big scheme, right? You don't really have to THINK. Which causes you to actually consider what you are about to do: spend money that is then GONE.
However, if your husband is like mine and virtually never spends anything out of pocket anyway (haircuts and the drive-thru meal once a week being about the extent of it), then it won't make a difference really. Does your husband take his lunch to work with him, or is he getting meals out? Does he make regular stops for coffee, or other small purchases like that (drive thru drinks, soda machine at work)? If he never spends then he likely can get by with using the card for his haircut, and a $20 bill for the week. If he is a nickel-and-dimer, then he needs to go all cash.