I am sorry to hear you are having this problem. There was recently a matchmaking update to the Playstation 3 version of Modern Warfare 3.
I recommend that you try having your friend host the party (by sending all of the group invites). This should allow you to join together in a lobby.
If you have any further problems beyond this, please let us know so we can continue to assist you.
Also, have you or your friend done any port forwarding for your Playstation 3's?
Have your friend try doing this;
(From the Playstation 3 Internet Browser)
Go to http://canyouseeme.org
In the empty box next to "What Port", type in 80 and select "Check."
Repeat the same process for 443, 3074, 3478, 3479, 3658, and 5223.
If those ports are coming back closed or timed-out, then this may be a factor as to why you guys are having this issue.
Please let us know what your friend finds so we can get this solved for you guys.