Depletion mosfet inverter
But I wonder, what if one of them is enhancement and the other is
  Depletion?


If, in the top picture, M1 was a depletion mode MOSFET, to turn it off you would need a gate voltage significantly lower than 0 volts. This means that a depletion MOSFET used in this type of complementary circuit would be ON for a greater range of the input voltage span and for a greater period of time both MOSFETs would be ON and conduct (potentially) a lot of current from the positive supply rail to ground. This of course is normally to be avoided.