Making two missions is always a simple option, but in this way you don't going to have some things like wherever Team 2 do will affect Team 1 chance of success...
Also most of the time we have a lot of people, and the number of big missions are limited.
Thats why will be good to have a new multi mode, something like "Team Coop".
I don't know how complicated will be, but (just given ideas to coders), take the TVT code, remove the who win/lose thing, also remove the team 1: Alpha, Beta, T2: Zeta, Theta, etc.... the rest could be the same as TVT with some adds:
-When you mark a ship as a "player" ship, you will also have to select if a ship of Team 1 or 2, (this is for removing the wing name need for teams as well it will fix the who can give orders to each AI)
-Comm menu will give orders to AI who are in your same team only (I'm not talking of Friendly, hostile, etc).
-Add a sexp to effectively disallow targeting and AI actions outside some range (to avoid targeting of ships too far away with radar = infinite and having AIs going to attack ships that are too far away).
-Add a "Use Team 1 data for Team 2", check box in brief, debrief, objectives and loadout.