This paper presents a novel interdisciplinary approach for the training of media scientists and engineers. The approach is being implemented at the Arts, Media and Engineering program at Arizona State University. Our graduates will produce new paradigms for the integration of computation and media in the physical human experience. Their work will result in hybrid physical-digital environments that address significant challenges in key areas of the human condition. The training model has the following characteristics: it is driven by research problems rather than by disciplines; it is based on an extensive interdisciplinary network; it is organized under the dimensions of research and application and promotes work at their intersection; it provides multiple paths for combining different types of disciplinary training with interdisciplinary training; it also provides a transdisciplinary training path. This paper presents the reasoning and implementation structures of these key facets, discusses our evaluation approach and presents preliminary results.