Using a Ginzburg-Landau approach, we study the interface fluctuations in ternary mixtures of oil, water, and an amphiphile. The capillary-wave spectra can be understood in terms of interfacial tension and bending rigidity of the amphiphilic monolayers. For large interface widths, the distortion of the interface profile due to curvature lowers the bending rigidity. The interfacial tension is found to depend crucially on the distance to neighboring membranes or walls. In particular, we show exactly that the interfacial tension vanishes in the infinite lamellar phase. The variation of the interfacial tension has observable consequences for a lamellar phase between walls, where we calculate the effect of the wall separation on fluctuation spectra and scattering intensities.