It's still "our" money. We usually split the bills right down the middle, in fact I end up paying for her car payment.
Again, we got seperate accounts because she was forced to open one up and maintain a balance with her semi-monthly automatically going to the account.
But, it does have its fringe benefits. I'll never understand why she buys $30 gold, snake-skin purses (exaggeration, but not really) or a fifth pair of black shoes...but this way I don't have to. And the same goes for her about my questionable purchases (did I really need the super charger? probably not...).
We both end up with a certain amount of disposable income that we can use however we choose.
I'm sure we would handle it if we had a joint account and a single pot of money, and it will become an eventuality when we start having babies and she has to quit her job (at least for a while, if not permanently) which means the "other" account would go bye-bye. I'm just saying it's nice to have that luxury right now.
But for the most part, I do still consider it "our" money.