As bob says, you just have to go to the load game menu and load the game as the other side (there is a button on the top right corner to show all the sides on a game). After you have issued orders to both sides (or three in three sides scenarios) just process the turn as any side.
Regarding Franciscus advice about the AI, beware because in many AJE scenarios there are several minor AI only factions (barbarians, pirates...). If you turn off the AI i think they will not do anything.
Really i think there is no need to turn off the AI to play both sides. The AI won't give orders to any side you have already gave orders, so there is no problem having the AI on. (at least i have never noticed problems with it on PBEM games).
Regards