The goal of the circuit below is to use a PMOS to turn an NMOS on and off which will blink the LED. A microcontroller is providing the square signal. Both MOSFETs are logic level and when I use them individually with the LED the behavior is what I expect. However in the circuit below when I send 5V to the gate of the PMOS the LED will just remain ON, but I expect it to turn off. Is it incorrect to wire the drain of a PMOS to the gate of an NMOS?
You need a drain resistor on the gate of M1. And by drain, I mean from the gate to ground.
The gate has a capacitance that needs to be drained off or the channel will remain open. Select a resistor size that will drain that in the order of magnitude of time that is reasonable for your application.