One way to reproduce it on a PC where the microphone does work is connecting a second microphone (make sure this one does NOT become the default one in Windows) and then try to get the game (using the ingame settings) to use the second microphone as input (impossible).

Personally I have multiple input-devices. For DayZ I need to use my USB microphone.

I tested changing my default audio input-device in Windows and DayZ indeed simply uses the default device.

So if you want to use the device that is not default that is not possible.

Usually you should just see a drop-down with all available input-devices so you can select the one you want to use in the software (DayZ in this case).

Additional information with later added screen-shots:
I made 2 screen-shots, one of the audio-settings in DayZ and one of the audio-settings in TeamSpeak 3. (Wanted to make a screen-shot of it in Arma3 but it has the same problem.)

I highlighted the option in TeamSpeak 3 that is missing in DayZ.

I can also confirm that this problem still exists in 0.30.113860