Effects of horizontal stochastic bottom structure on acoustic intensity in an isospeed ocean have been studied previously by the authors [J. Acoust. Soc. Am.76, 1445–1455 (1984)]. The bottom density and sound speed were taken to be random and ray theory was used. In this study we add a rough water–bottom interface, consisting of large‐scale, two‐dimensional random facets upon which small‐scale roughness may be superimposed. Each facet is assumed to possess small random depth deviation, slope, and curvature. Initially, we take acoustic rays to be specularly reflected from the facet bottom, and derive expressions for the mean and variance of incoherent intensity at a point receiver for a transmitted cw signal. The results are sufficiently general to permit their use with different bottom‐acoustic models, but we employ Mackenzie theory here. Relative effects of structure and topography are compared. Subsequently, small‐scale roughness is superimposed on the facets, and the added consequences of scattering are considered.