This issue happened to me while working on a texture pack:
The armor textures support transparency just fine, however once you enchant them only the "highest priority" part stays transparent, it's best to visualize this with screenshots(check the Attachment):
1. No Armor, fine
2. Diamond Armor, fine
3. Encahnted Diamond Armor, bug, only the chestplate is transparent.
4. Enchanted Diamond Helmet only, fine.
5. Enchanted Diamond Helmet & Shoes, bug, only shoes are transparent.
6. Enchanted Diamond Helmet & Shoes & Pants, bug, only pants are transparent.
As you can see it feels like there's some kind of "priority" system going on here, highest to lowest being Chestplate, Pants, Shoes, Helmet.
Edit:
Transparency doesn't seem to work on armor stands at all