An approach is introduced to interpret spin-polarized scanning tunnel microscope experiments in terms of differences in the tunneling conductivity with respect to different magnetic configurations and the corresponding band energy contribution to the magnetic anisotropy energy, the former being considered to be proportional to the applied external magnetic field. This approach is illustrated for Cu(111) coated with two monolayers of Co considering two types of Cr/W tips. It is found that the reorientation transition of the magnetization in the Co layers can unambiguously be identified even in cases when the tip contributes considerably to the tunneling current difference.