Soft x-ray resonant magnetic reflectivity measurements on thin films and multilayers in a {ital transverse} geometry using linear polarized photons are presented. Magneto-optic calculations taking into account the layer roughness allows us to reproduce all the experimental features of the angular and energy reflectivity curves as well as the asymmetry ratio in both cases. Application to Fe{sub x}Mn{sub 1{minus}x} alloy films epitaxially grown on Ir(001) brings more insights on the magnetic transition occurring at x=0.75. {copyright} {ital 1998 American Institute of Physics.}