This paper presents a model for the propagation of radiowaves through buildings. The model can be used as a seamless extension to ray-based propagation prediction models that only consider external reflection and diffraction, as do most current models. This involves the use of so-called transmitted rays, which are traced through building walls. Outdoor-to-indoor propagation (building penetration) is automatically taken into account as a "by-product". The transmission model requires no information about each building's interior other than a specific attenuation factor that describes the global behavior of the field inside the building. This coefficient can be determined for individual buildings by measuring the excess loss associated with the propagation path through the building. It is shown, however, that no large errors are to be expected if all buildings are characterized by the average of the empirical values obtained in this study, at 1.9 GHz. Path loss predictions generated with the aid of the new model are shown and compared with measured data to illustrate the considerable improvement in accuracy that can be achieved in realistic urban microcell scenarios by taking into account building penetration and transmission.