A solidify modifier generates a second surface parallel to the original and a rim surface that joins the two together. You can configure the modifier to use a different material for each of these two surfaces with the original surface using a third material.
We can create multiple materials for each object, the materials in this list can be referred by an index that starts at zero, so the first material is index zero, the second index one and the third index two.
In the solidify modifier, we can set the index for the second surface and the rim surface, the original surface will use index zero.
In this example, the generated surface is on the inside, we can change the direction of the normals to make the new surface be on the outside.