Recent attention to the effects of atmospheric turbulence on the interference of sound waves above both hard and soft boundaries has provided a spherical wave theory that allows for partial covariance between direct and ground‐reflected sound. Measurements of the interference spectrum at distances up to 45 m over a flat asphalt surface as well as measurements of jet noise over grass to a distance of 1100 m were shown previously to be in satisfactory agreement with the theory. The covariance between the two sound paths was estimated with one adjustable parameter by considering the transverse autocorrelation of the phase and amplitude fluctuations. The theory has now been further extended by considering explicitly, in addition to the transverse autocorrelation, the longitudinal autocorrelation of the phase and amplitude fluctuations along each path. At shorter distances of propagation it is found that the longitudinal autocorrelation, being close to unity, is necessary to estimate the partial covariance between the direct and reflected sound. At larger distances of propagation the longitudinal autocorrelation of both the phase and amplitude fluctuations goes to zero, contrary to the transverse autocorrelation which remains if the path separation is still of the same order as the correlation length of the medium. The new theory is compared with previous experimental results and yields essentially identical agreement as before but no longer requires an adjustable parameter.