How to Select both sides of double sided face?

I have a model with double-sided faces (normals facing ‘forward’ and ‘backward’ on the same face).
This was something I created in Sketchup 2013 and then exported double-sided (DAE) and imported into blender 2.69.
Now, if I select one of these faces, using face select right-click, and then assign that to a material. That seems to work until, I then … Select Inverse. the very same face (but i’m guessing the ‘other side’) is now (still) selected.

So the question is, how can I select both sides of a double-sided face?

Post screenshots and attach/post a link to your blend file showing exactly what you have and exactly what you want.

Face sin blender only have one normal direction

Well, what exactly means this “double sided”-tickbox in mesh panel?

Double sided is just a shading feature. It doesn’t create any new geometry that you can select. There are ways of creating two-sided materials, if that’s ultimately what you’re trying to accomplish, and it has nothing to do with selecting anything in the viewport. How exactly one does this depends on what render engine you’re using and what sort of textures you’re creating.