Hope this helps you, since you said you guys are just gonna play Mission...
There's 2 way to invite in a mission room:
Do you see on the right there's 3 tabs? "Mission", "All", "Buddy"?
Click on the "Buddy" tab and double click the player you want to invite, and a message should be sent over.
Or use the "Invite" function under the in-game search engine, click it and it should
open up your buddy list, and then you double-click the desire player to invite.
If none else works, just tell them the server#, room#, and even password if u want and let them join it manually.