In general, I would not put Elite in my army unless it is a *Elite.
I will keep my Elite in order to 'fish' Great leader, with the help of Arti and a bit of luck it should not be so scarce.
However when come the age of Modern Armor, it is so easy to get Elites units, that I will put them in the Army.
How does work a mixed army?
The game uses the best offensive unit in the army to attack.
The best offensive unit in the army will attack, using its own stats. If that unit loses as many hit points as its experience level would indicate, it retreats and the next best offensive unit takes over, and so on.
The converse occurs on defence, with the best defensive unit fighting until it loses its allocation of HP, then the next best, and so on.
In a given mixed army (an Elite Swordman, an Elite Archer, a Vet Musket and a Vet Spearman) the swordsman would always lead off when attacking, with attack strength of 3. If the army lost 5 HP while he was attacking, the Elite archer took over, now attacking at only 2 strength. If the army then lost another 5 HP, the veteran musket would start attacking. If that unit still lost another 4 HP - still in the same fight - finally the spearman would begin attacking.
This means that mixed armies can be of much use in the early game. Every time the army attacks, it does so with a fresh batch of HP assigned to the leading unit; the entire process is repeated anew for each combat. Even if a 14-HP army lost 6 HP attacking on one turn, the next turn the army could attack again and the swordsman would have five fresh shots with attack strength of 3, without needing to heal in-between. Basically, the swordsman could draw on the HP of the spearman and use it for strength-3 attacks.
The same thing can happen on defence, with the musket getting a full 4 HP worth of strength - 4 defence even against multiple attacks on the same turn (although the AI almost never attacked the army.)
Suppose you filled an early army with three horsemen, then load a knight into the army after building the Pentagon. When the army attacks, it will do so at 4 strength; and can make 2 attacks in the same turn both at strength 4 using only one knight, since the knight will get a fresh allocation of the army's HP assigned to it for the second attack.
Promotions are assigned based on whatever unit is currently doing the attacking or defending when the army wins the battle. This is why it is very hard to get a 19-HP army promoted to 20. For that to happen, the first three elite attackers all need to exhaust their 5 HP allocations, then the last veteran must win while the army has 4 HP or less remaining.
There is some weirdness when the army gets very weak, with the game switching active units in the army frequently during the army's last 3 or 4 HP. The best guess I can make is that each unit is guaranteed to have at least one HP assigned to it; attack with a 4-HP army and the best attacking unit will only attack until it loses 1 HP. But however that works, you can't really make use of it in combat.