A model previously developed for the statistical thermodynamics of microemulsion phase equilibria is used to treat the static and dynamic scattering by such systems. The random internal oil/water geometry is represented as resulting from a Voronoi tessellation, and temporal fluctuations are introduced by allowing the generating Poisson nuclei to perform independent Brownian motions. This dynamic model maintains the stationary statistics required of an equilibrium system and also allows representation of a continuous set of structures from oil-in-water to water-in-oil geometries including the bicontinuous geometries expected when oil and water are present in comparable amounts. Comparison of calculated scattering functions with experiment shows quantitative agreement with Rayleigh scattering data and at least qualitative agreement with measured space-time autocorrelation functions. Calculations of a k-dependent diffusion coefficient also are compared with experimental results.