A combined experimental and theoretical Brillouin light scattering study of thermallyexcited spin waves in Fe/Co multilayers with three and five magnetic layers in directcontact is presented. A large number of discrete, well-resolved peaks, classified as eithersurface or bulk standing modes of the stack, appear in the measured spectra. Theinvestigation of their frequency dependence on the magnetic field intensity and incidenceangle of light allowed us to determine the complete set of magnetic parameters of themultilayer. The interlayer exchange coupling and perpendicular interface anisotropy arediscussed in detail. The profiles of the dynamic magnetization associated with differentspin wave modes are calculated and utilized for the calculation of the Brillouinscattering cross section. The result, compared with experimental spectra, allowed thedetermination of the ratio between the magneto-optic constants of Fe and Co.