The presence of a partially reflecting screen on top of a grounded dielectric slab strongly perturbs its modal spectrum. The modes supported by such structures have been investigated in the literature for some specific, yet relevant cases. Here, a comprehensive modal analysis is presented, which emphasizes the inductive or capacitive nature of the partially reflecting sheet. The results of this analysis not only provide a clear overview of a wide class of structures of relevance in applied electromagnetics, but also unveil the presence of some useful propagating regimes so far barely explored.