Thermally-excited spin waves in double-layer films of FeSi/X/FeSi (where X=ZnO and SiO2) have been studied by Brillouin scattering. The thickness of the FeSi (2.6 wt. % of Si) layers is fixed at 1100±30 Å. Scattering from the Damon-Eshbach-type surface wave and the standing spin waves has been observed. The standing spin-wave structure of a 28-Å-thick SiO2 spacer is modified by interlayer exchange coupling, but not that of a 5-Å-thick ZnO spacer. The general trend of magnon frequencies as functions of the external magnetic field, the surface wave vector, and spacer thickness can be explained by the theory developed by Grünberg [J. Appl. Phys. 51, 4338 (1980)]. The Damon-Eshbach-type surface mode exhibits a systematic deviation from that theory at small surface-wave vectors.