The magnetic wave interactions on a thin film with interfaces having the profile of a periodic array of rectangular grooves are investigated. The film is assumed to be magnetized uniformly normal to the midplane. The technique is based on a transmission line model which is valid even for large relative depths of variation of the film thickness. When specialized to small relative depths of variation of the film thickness, the spectral characteristics of the power reflection coefficient determined by this large‐amplitude theory are in good agreement with those predicted by the existing small‐amplitude theories. The present large‐amplitude theory shows that the small‐amplitude theory gives the maximum of the power reflection coefficient reasonably correctly but overestimates the center frequency, the error increasing with the increasing values of the relative depth of variation of the film thickness. The investigation of the characteristics of the first two band gaps with the help of the present large‐amplitude theory reveals interesting features in the behavior of the band gaps as the relative depth of variation of the film thickness becomes large.