A scalar theory for scattering from multilayer coatings due to surface roughness is presented. A new model is considered which assumes that the roughness of the top surface of a given layer is due to the roughness introduced by the previously deposited layers and to the variations in thickness of the layer itself. The variations in the layer thickness are assumed to be uncorrelated from one layer to the next, but the roughnesses of the various surfaces are partially correlated. This model is compared to two existing models: one which assumes that the surfaces of the layers are completely uncorrelated and another which assumes that all of the surfaces are identical to that of the substrate. A fourth model is also introduced which assumes that the scattering is due to variations of refractive index within each layer. A matrix formulation for calculating the total integrated scattering and the change in specular reflectance and transmittance is presented. Predictions of the four different models are compared for several multilayer designs.