The predicted dependence of sound transmission on the statistics of the randomly rough interface between dissimilar fluids has been studied by use of the Helmholtz integral [J. Acoust. Soc. Am. 51, 1083–1090 (1972)]. The predictions have been verified for a plane wave passing from air through an aperture into water (laboratory model) and for radiation from a point source in air (laboratory and ocean experiments) for a wide range of surface acoustical roughnesses, R = k22σ2[(c2/c1)cos θ1−cos θ2]2. The roughness parameters σ,k ,c , and θ are the rms height of the surface, propagation constant, speed of propagation, and angle with the normal, respectively; subscript 1 refers to air and subscript 2 to water. When the surface is mirror smooth, the transmitted sound pressure is due to the change in divergence and change in impedance at the interface. For low roughness, R < 1, the mean-square transmitted pressure becomes decreasingly coherent with increasing frequency; its magnitude is decreased by the factor e−R compared to the perfectly smooth surface. For R ⩾ 1 the incoherent component dominates and the transmitted pressure depends also on the correlation length of the surface displacements.