Easy go to Private Match (beta) and on the bottom of the screen there is an option to switch teams select the team you wish to play as then leave private match select your campaign mission and there you have it.
very helpful I wish I knew the other day, cheers will help anyone who has completed the campaign but want's to replay certain missions for the achievement that requires you to be victorious on each mission on both sides. I needed to replay 2 missions on Milita and 1 mission on IMC but had to mess around backing in and out just to get the right team so cheers I'll be sure to let my mates know on Titanfall as they have been trying to work out if there was a better way,
