Hallo P Edson,

something is wrong with your circuit. Test output voltage after removing your LED driver circuitry. Are still 0.6V to be measured?
Normally such a high low-level output voltage is only measured, when a big current is driven into output. Then voltage drop accross turned-on NMOS output transistor will rise up. But from your explaination of driver circuit such a current cannot flow. So, there's something wrong with your driver circuit..

Bye,
Kai