Based on my observations, the armor values for the various levels runs as such:

Unarmored = 0 armor : Most militias, musketeers, Tercio Pikemen, arab units
Padded = 4 armor : Italian militia, Jinetes, other light cavalry
Light Mail/Splint = 5 armor : Mailed Knights, various swordsmen, Moorish miltia
Heavy Mail/Splint/Breastplates = 7 armor : Feudal Knights, SAPs, bodyguards
Partial Plate = 8 armor : Chivalric Knights
Full Plate = 9 armor : Late Bodyguards
Advanced Plate = 11 armor : Gendarmes, Gothic Knights

The most important jump is from unarmored to padded armor. It's a whopping 4 points. If you upgraded an unarmored unit to padded instead, it only gives 1 armor. Kind of lame really. There's also 2-point jumps from light mail to heavy and from full plate to advanced.

Say you take a unit of spear miltia and upgrade it 3 times to heavy mail. The graphic ingame shows them with shiny new helmets, steel breastplates/leggings and chainmail. But their armor reads as only 3. Take a unit that comes with padded armor when first recruited, like Italian spear militia. It starts off with 4 armor. Upgrade it 2 times to heavy mail as well. The same shiny helmets and armor. But they at least have a respectable 6 armor (it's still 1 less than they should be getting).

Some units are even more messed up. Tercio pikemen and musketeers/arquebusiers start of unarmored and their first upgrade level is not padded, it's light mail. So I upgrade them, expecting at least 2 armor, +1 for padded and +1 for mail. I only get 1 armor. With heavy mail and an identical appearance on the battlefield to fully upgraded pikemen, the elite Tercio pikemen have 2 armor compared to 3. I love using Tercio pikemen, but they take hideous casualties because their armor is so bad. I love using musketeers too, and if they had 5 armor like they are supposed to with the light mail upgrade then they could really press their advantage against enemy missile troops (their bullets would ignore enemy armor while their own modest armor protects them from return fire). As it is, however, unarmored troops (most city troops and advanced units) are unfairly gimped because the upgrade system doesn't take the huge jump from unarmored to padded into account, leaving a gap in armor protection between them and castle units (that mostly come with correct armor values) that they cannot close.

Please report this as a bug. I tried over at TWC but they are having problems with the site. A good temporary fix would be to simply give all unarmored units 3 armor to close the gap at the start, although it will not fix the light to heavy mail gap or the full to advanced plate gap.