My wife handles our groceries and such. We actually have two separate accounts: "mine" gets the paycheck, pays the bills, and transfers money to "hers" twice a month.
We also have a third "giving" account that gets a bit of money set aside to give to or buy things for other people. This can be anything from a car repair to just buying someone lunch.
Direct debit is fine if you trust the other side not to screw up and charge too much, leak your credentials, etc, but I've seen exactly that happen several times. You're basically giving them to withdraw as much as they want from your bank account.