In the paper, the influence of interface anisotropy on the spin wave resonance (SWR) characteristics has been investigated and the accuracy of sample preparation necessary to compare the experimentally obtained SWR spectra of magnetic multilayers with theoretical predictions has been estimated. The transfer matrix approach has been applied to the calculation of the energy and relative intensities of SWR spectra as a function of the spacer thickness. The oscillatory exchange coupling between two ferromagnetic layers through nonmagnetic f.c.c. spacer has been employed to investigate spin wave profiles. Various pinning conditions at the external surfaces have been considered and the role of interface anisotropy have been discussed in detail. The results obtained show that for very thin spacers, the difference of one monoatomic layer of the spacer thickness can significantly influence the character of the spectra obtained. It has been also found, for the wide range of interface anisotropy parameters, that for thicker spacers (d greater than or equal to 10 monoatomic layers), where the interlayer exchange coupling is rather weak, the interface anisotropy is the main factor determining the parameters of SWR spectra.