You are trying to drive the lower MOSFET when its' source terminal is connected to a negative supply rail, and the 555 timer is connected GND to ground. That will never work. As soon as the lower rail starts dropping more than ~3v below ground, the lower MOSFET will turn on, and you won't be able to turn it off.
Ask yourself, how will your circuit get the Vgs to 0v when S is tied to a negative voltage?
Also, you must stop thinking of gate voltage in any other terms than Vgs; that's voltage on the gate referenced to the source terminal. The MOSFET really "doesn't care" about the outside world too much, but if you exceed ±20v Vgs, your MOSFET will die.