Given a rough interface between two fluids of different densities but similar sound velocities, we assume that the mean dimensions d and spacing h of the roughness elements is small compared to an acoustical wavelength, i.e., kd<kh?1, where k is the wavenumber. If these elements are hemispheres based on a plane z=0, one may express the diffracted field of each element by Rayleigh’s approximation; the use of classical integral theorems then allows one to replace the summed effect of these contributions by a simple linear boundary condition applied at z=0. Minor heuristic corrections allow one next to extend the result to roughness elements of other shapes and, by averaging, to stochastically rough surfaces. This technique was first introduced by Biot in the context of a rigid boundary and is generalized here to a rough interface between two fluids, giving two boundary conditions. The first states the continuity of vertical fluid displacement along a fictitious smoothed surface z=0 with an added correction which is first order in a roughness parameter of order kd. The second condition is the continuity of pressure and is, to within second-order terms, identical with the usual smooth boundary condition; in a first-order theory, then, this condition is the usual continuity of pressure at z=0. Use of this pair of boundary conditions shows that the body (volume) acoustic modes behave as in the smooth interface case, with the addition of corrections of order kd. It also demonstrates the existence of a slightly dispersive boundary wave mode traveling along the interface, and of order kd. Both are intrinsically first-order effects of coherent multiple scatter by rough surfaces; both include the effects of steep-side roughness elements and are not obtained in other theories of rough surface scatter. Use of the normal coordinate technique enables one, furthermore, to obtain new closed-form solutions for the boundary wave and the body (volume) wave fields that are first order in kd. The boundary wave amplitude decreases with range r from the source like r−1/2, in contrast to the body waves which fall off like r−1 or faster; it may thus dominate for sufficiently large range. This phenomenon has, in fact, been verified experimentally for the case of a rigid rough boundary, by means of model work in an anechoic chamber, in earlier work by Medwin and collaborators. It suggests interesting posibilities in geoacoustics and in underwater sound in particular, e.g., the propagation, under suitable conditions, of substantial low-frequency energy into regions of acoustic shadow.