We present an interface model based on two-scale homogenization to predict the coherent scattering of light by a periodic rough interface between air and a dielectric. Contrary to previous approaches where the roughnesses are replaced by a layer filled with an equivalent medium, our modeling yields effective jump conditions applying across the region containing the roughnesses. The validity of the model is inspected by comparison with direct numerics and with experimental measurements on an air/silicium rough interface near the Brewster angle. It is shown that the interface model reproduces accurately the shift in the Brewster phenomenon without any adjustable parameter, which is of practical importance in retrieval methods to get thickness or filling fraction with reliable physical values.