All combinations of the two things are possible, at least in theory. A monoracial, monocultural society . Japan, for example. The Scandinavian nations are similar. A monoracial, multicultural society .
Obvious cases are Lebanon and the old Yugoslavia.
Nigeria, with its Christian South and Muslim North, also fits here, I believe. A multiracial, monocultural society . The U.S. is the outstanding example, with some qualifications noted below. A multiracial, multicultural society . Some people might say that the U.S. is closer to a type four than a type three.