Mixturelean
- the problem is almost certainly incompatibility between the microphone insert in the headset the passenger is using and yours. If passenger unplugs his/her mike, yours is fine, yes?
When you press the transmit button, that disconnects all microphones but your own, so the problem goes away and ATC can hear you fine.
Ideally, some measurements would be useful before opening up the headset and soldering. If you can get two or three different "OK" headsets, measure the "resistance" of the microphone lines of them all (with the meter leads both ways round in case the mike is polarity sensitive). (There are snags with some electret mikes with preamplifiers, but that's getting complicated).
If the pax one is indeed a lot lower resistance than the others, try inserting about 220 ohms in series with the mike line - in the plug or in the junction box. If that sorts it, stop there. If that sorts it but that headset now can't be heard loudly enough, try a 22uF or thereabouts across the 220 ohm resistor.
It's a case of experimentation to find the best component values. I don't know anyone who's tested them all and knows the right resistor/capacitor values for all types.