How would I make the unpainted part of a texture paint image not affect object color when mixing? I am trying to model a face in Blender. 

I am having an issue where I am trying to use texture paint to make the lips red. I have already set up a procedural skin texture for the head, which works perfectly except it also makes the lips skin-colored.

In order to fix this problem, I tried to texture paint on a red color. Unfortunately, when I created the image for the texture paint, everything was black. This made it impossible for me to combine the procedural skin texture and the texture paint image into the base color of the face without severely darkening the rest of the head.

See if this image helps:
Use a math node set to "Less than" with a very low threshold, and use that in the factor input of the mix RGB.

Illustration :