Thank you meetar for finding and posting it!
The 'two sided lighting' work around works for some situations and is probably the simplest way.
What the post also said, is that there is a tool in the 'bonus tools' which does the trick. And there really is!
It's called 'Normal Checker' and it creates an instance of the mesh, reverses its normals, assigns aother shader and switches 'double sided shading' off on both instances. The result is almost exactly what I was looking for: The outside of the faces seems to have one shader and the inside another.
After using the tool I can simply delete the instance labeled 'inverse' and check 'Double Sided' in the Render Stats again.
Oiginally it was probably intended as a way to check if the normals point into the right direction.
Thanks again meetar!