Just a note, Domein's suggestion is what UFO: Aftershock's (and possibly with other UFO After games) currently does.
In UFO: Aftershock
Max hp is what is damaged slowly each hit. It requires a treatment facility to restore. If you are unconscious, all damage is done directly to Max hp, and if this max hp reaches 0, you're dead. While you are unconscious, your max hp slowly decreases until you are revived by a medikit, or completely dead.
Current hp is the amount of hp you have that keeps you conscious. It is damaged by every hit, explosion, and whatnot a lot faster than max hp. If current hp reaches 0, you are unconscious.
Stun reduces current hp only, and has no effect on max hp.
Acid and fire and other things rapidly reduce both current and max hp (current still faster though). This is sorta like bleeding while still conscious.
You can't bleed while conscious though, only when you fall unconscious do you bleed to death.
Medikits can't raise your current hp above your max hp.
Just thought I'd mention where this idea has already been implemented..
One other note is, if the mission ends, and any of your soldiers are stunned or bleeding, they are considered lost. I didn't like this idea so much, but that's how it was implemented. Unconscious soldier = dead soldier, whether the mission was a success or failure.