Or another way of thinking about it....if the account is overdrawn sooner or later those pesky $39 dollar overdraft charges are going to start popping up in the mail. So it may cost you to not cover the overdrafts.
On the split accounts...there is a certain psyche relationship theory that separate checking accounts is actually better for a relationship. It seems that many people relate their bank accounts to their personal identity. So having separate accounts promotes a personal independence of sorts. Then from there they suggest a third joint account that is purely for paying the bills. Each spouse makes payments to the joint account...thereby quantifying what they bring to the relationship financially. This actually promotes interdependence in that you are working together in a quantitative manner to pay the bills.
I would add that setting up a joint savings account for vacations and such is taking it even further. Discuss a vacation destination, figure out how much you need to save to go there, and then work together towards the goal of filling the savings account to that amount. Each deposit will be visible to each and will be seen as working together towards a joint goal with visible evidence that you are both working towards your goal. (Your kids are old enough to contribute and could join in this also...that way it isn't a relationship thing, but a family thing)