Transparent pixels on inner layer of skin renders as black

I downloaded a skin and applied it to my character. The skin has transparent pixels on the inner layer.

What I expected to happen was...:
Those pixels would be transparent

What actually happened was...:
Those pixels rendered as black in both the launcher and in-game. The bug still happens when I run Minecraft without mods.

Steps to Reproduce:
1. Apply the attached skin

2. The skin should show the black pixels both in the launcher and in-game

Screenshots

The first screenshot is what the skin looks like on Planet Minecraft. The second screenshot is what it looks like in-game. Notice how the transparent arms and feet turn black in-game: