My wife and I file zero on our taxes and we have two kids. Should we be filing something other than zero?

My wife and I claim zero on our taxes and we have two kids. Should we be claiming something other than zero? When we file our taxes we file married filing jointly. Usually before we get to mortgage interest, daycare costs, and other deductables we are owing a ton. Can we file married filing separate or should we be claiming something other than zero?