Recent work by Milder [J. Acoust. Soc. Am. 89, 529–541 (1991)] has shown that increased efficiency in evaluating the Helmholtz integral equation for scattered fields may be obtained through a method known as an operator expansion (OE). More recently Kaczkowski and Thorsos [J. Acoust. Soc. Am. 90, 2258 (A) (1991)] have validated the accuracy of the OE for a broad variety of impenetrable 1-D rough surfaces. Here the OE formalism is used to obtain results for penetrable, even acoustic–elastic interfaces. Since in penetrable problems neither the value of the scattered field nor its derivative on the interface is known, it is necessary to seek some approximation. In this work a modified Kirchhoff approximation is proposed, where the scattered field on the interface is approximated by the incident field multiplied by the local reflection coefficient, but its derivative is approximated using the operator expansion. Two-dimensional scattered field realizations computed using this procedure are compared to exact fluid–fluid results obtained by a boundary integral approach and fluid–elastic results obtained by the boundary element method of Gerstoft and Schmidt [J. Acoust. Soc. Am. 89, 1629–1642 (1991)]. Conclusions are drawn concerning the accuracy of the method and the feasibility of using it to estimate three-dimensional reverberation.