Also, it's even more confusing as they are separate yet they are displayed (as far as I remember) in almost the same way.
Yes, the user, especially the new user does not really care if they are different things, peer to peer or server side, really. User is just confused in alien interface and has a bad experience. It calls for a fix.
I suggest the following:
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add check to starting mission that if no peer to peer party is present checks if user is logged in to the server
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when true, add check whether he is in a party on server side (if many parties present, count only the most recent party)
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when true, add pop up window to ask whether the user wants to start peer to peer party with people in current server party to make a campaign valid party
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if user said yes, make the right, peer to peer connection party identifying users thanks to server and start the mission with party.
It's really not that difficult to make it intuitive to use.