Why can I only invite my friend to a party and nothing else?

There are a couple things that you need to check. The first one is to check your online safety and privacy settings. Please access the following link to make sure they are well adjusted => Manage Xbox online safety and privacy settings | Xbox Support.

The second thing that you will need to make sure of is that your NAT type is open. If the NAT type is not open, you will need to open some ports with your internet provider. These ports must be open for Xbox Live to work: Port 88 (UDP) Port 3074 (UDP and TCP) Port 53 (UDP and TCP) Port 80 (TCP) Port 500 (UDP) Port 3544 (UDP) Port 4500 (UDP).

If you’re still having trouble joining an Xbox Live party, someone in the party might have a Network Address Translation (NAT) problem. To find out, have everyone in the party test their Xbox Live connection. Here’s how:

1. Press the Guide button on your controller, go to settings, and then select System Settings.
   
2. Select Network Settings.
   
3. Select Wired Network or your wireless network name (if you're prompted to do so).
   
4. Select Test Xbox Live Connection.
   
5. If you’re signed in to a profile, select Yes when notified that testing your network connection will sign everyone out, and then select Continue.
   

After going through the troubleshooting steps mentioned, I invite you to perform a quick power cycle by turning off the console and then unplugging all the cables. After 2 to 3 minutes, re-plug them back again, then restart your console.

why can't I join a game from a friends invite? I friends cannot join from my invites, but we can all party up. I don't have elite and it was only affecting MW3.

The problem is not with friends. People on my friends list can invite me. People who are not on my list can send me messages but nothing else.

Same issue here man. I cant play co op with my friend from australia, we can play every other game but DR3. Every time i send an invite it tells me failed to send invite we also cant keep a Dead Rising 3 party together. If i or he is alone in a party it
becomes a dead rising party but if any one of us joins it turns back to a your party. Same with the invites because if i invite him it turns to a DR3 party but turns back to a Your Party and tells me that the invite failed to send. I can keep a DR3 party and
play with everyone else except for him and another friend please help microsoft. Ive had DR3 since launche and havent been able to play with my good friend.

Party Chat doesn't default to private (which is really an "invite only" setting). The default is that anyone on your FL, or friends of friends, can jump in. You have to manually set parties to invite only.