The microphone won't work with the headphones plugged in (They're the ones that came with it). The microphone works without it plugged in and the headphones still emit sound perfectly fine.
I'm having the same issue. My phone is a Galaxy S6 and the microphone will work fine when the headphones are disconnected. I've tried numerous pairs and cannot talk with them plugged in, though last I checked, have no issue if plugged into the auxiliary cord in my car. None of the pairs I'm using have a build in microphone that I know of and one pair is the original pair that came with the phone.