On the Steam version, it is impossible to swap out alive characters as the game's exe is based on the original release, in addition the changes to the game makes it impossible for the official patch to work on the steam version. (If you swap out characters, the game will automatically change them back once starting a mission.)

It looks like this issue is still not fixed. So frustrating...

Same issue here, can't change characters between missions, even if you change them in the briefing, they will bring back your older team once the mission begins. Very annoying, you must stick with the same team throughout the game.