Scattering characteristics of multilayer fluoride coatings for 193 nm deposited by ion beam sputtering and the related interfacial roughnesses are investigated. Quarter- and half-wave stacks of MgF(2) and LaF(3) with increasing thickness are deposited onto CaF(2) and fused silica and are systematically characterized. Roughness measurements carried out by atomic force microscopy reveal the evolution of the power spectral densities of the interfaces with coating thickness. Backward-scattering measurements are presented, and the results are compared with theoretical predictions that use different models for the statistical correlation of interfacial roughnesses.