Can you definitely have coop in those PVE matches?
I did 2h last night... you select PVP or PVE server (PVE is called Joint Ops) and choose 1 of 3 factions (pretty sure it makes little to no difference, at the moment, except where your home base is, but you can only groups up with members of your faction!).
It looks like you can see all the players on your faction on the map (blue markers on the map) and can group up with friends of randoms or just play solo.
At the home base, bring up the map (long M press) and click on a destination LZ (the choppers are like fixed taxis... they take you from A to B and kick you off the chopper when they get there).
The chopper comes into the base, you get on and it goes.
You can get on a.n.other chopper, nothing stopping that, so I ended up at India LZ, much further north than I had intended, but grabbed some loot and extracted
Definitely co-op without PVP (is there Friendly Fire from group members?) if you choose Joint Ops.