D&D 5E (2014) Blade Ward & HAM

[Corwin]

Only if you don't know how to use it properly.

Ain't that the truth... in so many things in life...

 

[Blue]

Visualize what's happening.

Unfortunately the PHB doesn't give much of a visual description of what Blade Ward looks like...
I used to think that dozens of spectral daggers appear around you deflecting some blows.

In any case, being a ward it means that it's something outside of yourself, like a force field, which means that whatever weapon reaches your flesh, it first crosses this ward and then your heavy armor.
(Of course you could view this ward as a thin barrier over your skin, which would change the order of effects... but I wouldn't call that a ward)

With Stoneskin however, its resistance is the last one to be applied, because as the spell says it turns your skin into stone. Which is under your armor.

Actually, there are specific rules in the PHB which [MENTION=60210]jaelis[/MENTION] quoted that give the order. First subtract, then halve.