Drop-in/Drop-out should work fine.
1) I recommend starting the game with both human players so you both get homeworlds (one can start later, but will only get a home command core, not a whole planet, but this is still a generally tenable position if your difficulty isn't too high).
2) After that, if one of you needs to stop but the other wants to keep going, you can use the Manage Players button on the in-game menu (press escape from a normal view, then click Manage Players) to disable the guy who left. Or you might have to disable the second player, I honestly forget if it works to disable the first player and thus play the second one... But either way the still-active player can control all the units of any disabled human players.
3) You can also do this when loading a save: if it was saved in MP it will say "Waiting for Players" but you can use Manage Players to disable the ones that it's waiting on but aren't coming
4) When you want to join up again, have first player load the save and (if not already done) use Manage Players to re-enable the second player, and have the second player join normally.
Note that if you're both wanting to play solo during the interludes and you want the progress of both solo jaunts to be reflected when you pick it up in MP again you'll need to actually hand the save file back and forth, there's no mechanism for "merging" two distinct savegames into one
If you run into any problems please let us know and we can probably fix it.
But suffice it to say, there are several folks around here who play running MP games in a similar way as what you're describing (if I understand you correctly).