We study the homogenization process of ferromagnetic multilayers in the presence of surface energies: super-exchange, also called interlayer exchange coupling, and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequence of extension operators for the multilayer geometry. First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction is...