An analytical expression for the two-frequency, two-position, two-time mutual coherence function applicable to propagation through thick random media with nonuniform electron density and plasma velocity is derived using the phase-screen/diffraction method (PDM). In this method the ionization is collapsed to a number of thin screens and diffraction is developed in the free space between. The resulting mutual coherence function converges rapidly to the continuum result as the number of screens representing the medium is increased. The effects of multiple scatter occurring over long distances and varying plasma velocity over the propagation path are shown to be important in HF propagation. Scattering functions (delay-Doppler power spectra) obtained as Fourier transforms of the PDM mutual coherence function are compared to scattering functions measured by an HF channel probe. Nonuniform velocity profiles are shown to account for the variety of delay-Doppler couplings observed.