The electronic structure of three monolayers (ML) Co on Cu(111), grown with Pb as a surfactant and capped with two ML Cu, was studied using magnetic circular dichroism in valence-band photoemission. The easy axis of magnetization in these films is perpendicular to the surface, allowing an experimental setup of extreme symmetry (photon spin, light incidence, electron emission, and magnetization all aligned and perpendicular to the surface). In such a geometry features observed in magnetic dichroism can be directly related to the symmetry character of the relativistic band structure. Experimental data in the photon energy range of 6-24 eV are presented. The observed magnetic dichroism and its dispersion with photon energy can be explained on the basis of direct transitions in a bulklike band structure of Co.