As it stands, the majority of the modes in "Call of Duty: Modern Warfare 2" multiplayer do not support Xbox Live's party chat option. In fact, the only ones that do are Free-For-All, No Party Team Deathmatch, Ground War and two of the 3rd person modes. If you're only interested in chatting with friends while playing the other modes, you'll have to manually mute everyone else in your game (including any newcomers), or do this:
Step One: Go to Xbox.com and log in to your account
Step Two: From your profile page, click on Privacy Settings (it's just to the right of your avatar)
Step Three: The top option should say Voice and Text. Set it to Friends Only. Save.
Now whenever you play "Modern Warfare 2" multiplayer you'll only hear people you are friends with.