The roughness of the interfaces in a series of (AlAs)n1 (GaAs)n2 (AlAs)n3 (GaAs)n4 superlattices has been measured by comparing the Raman frequencies of the confined GaAs-like LO phonons with results from a linear chain model modified to incorporate a description of the roughness. A new model is developed which shows that the interface roughness parameter W of a layer of average thickness n monolayers can be described by the expression W2 = αnns/(αn + ns), with α = 1 and ns = 2 and 5 for GaAs and AlAs, respectively. © 1994.