The issue is indeed with your connection/router.
Even if you have just a modem, some modems have a build in router and that messes xbox live up.
It took me awhile to figure this out and how to get voices working.
My example is, that any game I joined with friends, I couldn't hear some friends/other players.
First, do an xbox live network test and look what the NAT says...if it's moderate or strict, most likely that's your problem (mine was strict).
The reason in a nutshell, is that you cannot reach a player behind strict or moderate if you are behind a strict nat, moderate to moderate nat sometimes doesn't work either. The best test is, can you do a private chat with that player? If it's a router/network issue, you will be able to make the chat, but you won't hear the other party.
I first tried to do port forwarding from my router to the xbox360, but with no luck. It seems the port forwarding will only work if you are behind a moderate nat.
There is no other way to fix a strict issue, than to enable UPNP on your router/modem.
If you just have a "dumb" modem with a router, you will need to enable UPNP on your router. Mine is an airlink, and it was hidding in the system settings (I have comcast).
One of my friends with with Verizon dsl has a setting in their "services" menu in the modem where you can check off enable UPNP.
This fixed any communication and problems joining/hosting games for myself and my friends (when I test my nat, it now says OPEN, not strict anymore).
That reminds me, another way that shows you have NAT problems, is that you try to join a random game and it says something like "connection lost to host" even before you get into a game. It's very apparent in GOW when you do a quick game and it says can't connect.
This is what worked for myself and my friends, but like the previous posters, it might also be a problem with your mic
If you are paranoid...UPNP isn't 100% safe, if you get a worm or virus, it can open ports on your router, just like xbox live does when it uses it, but it's only possible if a device INSIDE your home network gets infected.
Hope that helps...