The problem of reflection of polarized light at any angle of incidence by multilayer magnetic and dielectric films is solved in specific cases by summation of reflected components, and in general by recursive application of the specific solutions. The Jones matrix convention is used to describe individual interfaces where the elements of the Jones matrix are the Fresnel coefficients for the reflecting (or transmitting) media. An explicit model, in terms of material parameters of individual films and film thicknesses, is presented for a system of n films, any of which can be magnetic or nonmagnetic. Also, limiting cases of zero magnetization and vanishing layer thicknesses are examined.