PS3, Modern Warfare 2 Parties.

So, me and two coworkers are playing modern warfare 2 on the PS3, we want to form a party so we stay on the same team all the time.I cannot join Coworker 1 or Coworker 2's party.
Coworker 1 can join Coworker 2's party if inivited.
Coworker 2 cannot join Coworker 1's party if invited.So I'm stuck here outside the party all the time. We get the error "Cannot connect to host".I connect through a wireless linksys router which goes to my cable modem.
The game lists my NAT type as "Moderate".I don't know the details behind my coworker's setup, but I believe they told me their games list as NAT type "Open".Is my router causing the problems?Edit:
I tried accessing my router's setup, and noticed the web interface was excruciatingly slow, so I rebooted my router. Now MW2 lists my NAT type as Open. Tomorrow I'll have to try again with my coworkers and see if it works correctly.