This sounds like a job for a Noise Gate. Applied to your microphone track it will mute the track whenever the sound level in the track falls below a specified level, thus muting your co-host’s voice on your track. Is that what you want?
You can get a noise gate plugin here. Be sure to read the instructions provided either in the zip file, or provided within the plugin.
This is a Nyquist plugin. For instructions on installing Nyquist plugins look here.
– Bill