I find this issue very odd because of issue I have with my microphone and have to use my Kinect to communicate with everyone and Search & Rescue is my favorite game mode.
The issue is that you cannot play while in party chat which is understandable however this game mode will not let you play if you have to use your Kinect to communicate. I hate to do it but my microphone is *** up and having lots of issues.
Another issue is that if you are playing using your microphone and you need to plug in your controller to charge you'll be kicked because the controller takes a few seconds to initialize and cuts off the headset which will also kick you from the game. The same thing will happen if you happen to unplug you microphone while in game.
They could/should probably issue a buffer time period of about 10 seconds before you get kicked so that you have time to plug in your controller and it gets initialized or something.