A consistent environmental‐acoustic model for a deep moving ocean is formulated. The acoustic model for regularly perturbed SOFAR rays is approximately solved using a type of WKB  (J) expansion. Interfacing conditions between the hydrodynamics and acoustics are developed which lead to constraints on acoustic frequency and transmission range. As an application, transmissions are considered through stochastic internal‐wave fields, which have been modeled in a previously published paper by the authors. Formulas for ray phase variances are derived. These formulas are asymptotically evaluated for rays with relatively significant depth variation, using the stationary phase method. New results are obtained for the dependence of the variances on internal‐wave primitives, such as energy spectra. Expected multipath intensity is calculated for transmission through an ocean with static state modeled by a bilinear sound‐speed profile. The effects of the internal‐wave field and of varying internal‐wave parameters on the expected intensity are shown to be significant.