In the Solidify Modifier you have set Normals to Flip. This in combination with having the Material Offset to 4, which refers to the fifth material slot (counting starts at 0, but since you have only two materials 0 and 1 the highest number is used) results in using material 1 for all visible faces.
Just for info on the Material Offset and Rim materials: like the word "offset" implies, it is always the slots offset based on the faces material. Which means, say Material Offset is 1 and Rim is 2, than a face which uses material slot 0 will get slot 1 for the solidified face and slot 2 for the rim, whereas a face using e.g. material slot 2 will get slot 3's material for solidified faces and slot 4 as material for the rim. If you now set Normals to Flip, the solidified face shows the assigned material but the original face shows the offset material.
When using only a single material or by resetting the Material Offset to 0, this problem will disappear and show the correctly assigned materials. However, flipped normals can also cause other problems with materials in rendering and for physics simulations etc. so you should rather disable the Flip option (this also enables you to still use the offset if you need it for special materials on the solidified faces).