Can a face have two sides? I want to be able to texture both sides of a face.

No, Because, when the reduce feature will use one of them will removed. If you wish do something like that you must use two different faces closer but not at the same location.

Yes, Enter in face mode and select just ONE of the faces you want to make double sided. F9, then click on twosided button.

Blender's render engine can use double sided faces but many others can't. If you use the models you make in Blender for other application plan on double sided faces not working.

I just came back to this thread to ask what double-sides actually did do, because they weren't acting how I wanted them. I missed the last reply in this thread. Chalk Poser up as an application that doesn't use two-sided faces from Blender. Which is a pain. Poser requires objects to be in such a small scale in the first place. Adding second sides to things almost requires instruments that can measure objects on an atomic level.

"I just came back to this thread to ask what double-sides actually did do, because they weren't acting how I wanted them."

double face means that the face will be visible from both side.
By default, in blender or in Poser rendering shows both side of a single face.
But in Blender video game or with Poser in preview mode only one side of the face will be visible.
The one identify by the rotation direction of the point creating the face (FYI).
Be care, if double faces works fine in Poser4, I am not sure it will works fine in next releases.
"Adding second sides to things almost requires instruments that can measure objects on an atomic level."
No, UVmapper have a feature to do it. But I do not remember if this feature is only available in the commercial version or in the free version too.