Is the radio antenna in the windshield for a 2011 Mercury Grand Marquis

No. Ford, Lincoln nor Mercury have it in the windshield. Usually, it's part of the grid-work in the backlight (rear window) along with the defroster grid.

Also you cannot have the radio on while the rear window defroster is on. You can listen to a CD or Tape but not FM or AM radio while it is on.

Weird! That's probably going to take some digging around. Sounds more like a wiring concern now. Aftermarket radio? I could be hooked up to the wrong circuits for power and ground.

I have the stock radio (and my Grand Marquis is a 2003) I know that when both are on, the radio goes to static.

Sorry, your original post says 2011. The only other thing I can think of is a Ground concern. You could try cleaning up all of the ground wires and connections near the battery. Disconnect them, clean them all up and reconnect them. It's worth a try and won't cost you anything.

why does my car radio swiches channels on its own

HOW CAN YOU TELL IF YOUR CARE RADIO IS BROKEN