Here's the procedure ver batim from the Haynes manual for a Taurus, not
sure what kind of car you have but should be identical:
The evaporator core on most vehicles is hard to access, and dealership
service departments have a lenghtly procedure to eliminate the fungus
by opening the evaporator case and using a powerful disinfectant and
rinse on the core until the fungus is gone. You can service your own
system at home, but it takes something much stronger than basic
household germ-killers or deodorizers.
Aerosol disinfectants for automotive air conditioning systems are
available in most auto parts stores, but the most effective treatments
are also the most expensive. The basic procedure for using these
sprays is to start by running the system in the recirculation mode for
10 minutes with the blower on its highest speed. Use the highest heat
mode to dry out the system. Keep the compressor from engaging by
disconnecting the wiring connector at the compressor.
The disinfectant can usually comes with a long spray hose. Remove the
blower motor resistor, point the nozzle inside the hole and spray,
according to the manufacturers recommendations. Try to cover the whole
surface of the evaporator core by aiming the spray up, down and
sideways. Follow the manufacturer's recommendations for the length of
spray and waiting time between applications.
After the evaporator core is cleaned, the best way to prevent the
mildew from returning is to make sure your evaporator housing drain
tube is clear.
Hope this helps!