Strict: Can only play with people with OPEN NAT
Moderate: Can play with people with MODERATE or OPEN NAT
Open: Can play with ANYONE
If you are open and he is strict he should be able to join you. But if you have someone else in the party or even match with a MODERATE or STRICT NAT then it won't work.
That said, I'm moderate and have tried many ways to change mine with no luck. Sometimes I have problems getting kicked if I'm in a party (not the host) and we all join a match it sometimes pushes me out of the match. It never does if I'm the host.
Try having him host the game and everybody join his party prior to match. It will take longer for him to find the match, but once you do your set. If you are OPEN and he is STRICT and you cannot join him IDK what it could be. Moderate gives me crap sometimes (mainly in COD: Black ops) so I don't even want to imagine what STRICT is like.