Specular microfacet distributions have been successfully employed by many authors for representing materials glossiness, and they are generally combined with a Lambertian term that accounts for the colored aspect. Such a representation makes use of the Fresnel reflectance factor at the interface, but the transmission factor is often ignored. In addition, the generalization to microfacet distributions with a more general reflectance is known to be complex, since it requires to solve an angular integral that has no analytical solution. This paper proposes a complete framework for physically handling both reflection and transmission with microfacet distributions. First, we show how transmission affects reflectance of an interfaced Lambertian model, and provide an analytical description of an individual microfacet reflectance. Second, we describe a method for handling distributions of such microfacets in any physically based Monte-Carlo rendering systems. Our approach generalizes several previous models, including flat Lambertian materials as well as specular and Lambertian microfacets. The result section illustrates the wide range of materials that can be possibly taken into account with this representation.