My app uses the microphone and outputs audio, so I am setting my Audio Session to the Play and Record Category, but this seems to disable Airplay. If I set the category to Play,
What AirPlay device are you trying to use? Does it have a microphone?
If not, iOS won't present it as an option when using the PlayAndRecord category, because that device can't play and record. It would show up when using the Play category though.
Also, if the device you are using is a Bluetooth device, have you set AVAudioSessionCategoryOptionAllowBluetooth to YES?