In some cases, audio communications may only work one-way on the Xbox console when playing multiplayer online. The user on console B is able to hear the user on console A, but not the other way around.
This typically occurs if a player has their Xbox communication privileges set to "Friends Only", and are signed in on an inactive quadrant.
This issue should be resolved by either moving to the primary quadrant, or setting voice settings to "Everyone".
Information about Xbox 360 Privacy Settings can be found at the following location: