Sorry, can't provide screenshots atm, but I can describe in detail.

Basically whenever a piece of armor with additional custom attributes aside from "generic.armor" is put on your body in survival mode, the armor display above your health will only include the armor value of that piece. Kinda hard to understand, but here's instuctions to replicate:

To replicate:

1, use this command on yourself:

"/replaceitem entity @p slot.armor.head minecraft:diamond_helmet 1 0 {Unbreakable:1,AttributeModifiers:[{AttributeName:"generic.armor",Name:"generic.armor",Amount:4,Operation:0,UUIDLeast:1l,UUIDMost:1l,Slot:"head"}]}"

2, use this command on yourself:

"/replaceitem entity @p slot.armor.chest minecraft:diamond_chestplate 1 0 {Unbreakable:1,AttributeModifiers:[{AttributeName:"generic.armor",Name:"generic.armor",Amount:10,Operation:0,UUIDLeast:1l,UUIDMost:1l,Slot:"torso"},{AttributeName:"generic.movementSpeed",Name:"generic.movementSpeed",Amount:-0.8,Operation:1,UUIDLeast:1l,UUIDMost:1l,Slot:"torso"}]}"

3, go in survival and take off the helmet and your armor bar will apparently shoot down to 0, even though you have pants on.

4, If you then remove the pants and re-place them on yourself, the bar will fix to the total of the pants.

5, and of course, if you add the helmet again it will go to 4.