Coronagraph focal-plane occulting masks have generally been described as attenuation profiles free of any phase shift. However, phase shifts are expected and observed in physical occulting masks, and they can impose significant limitations on coronagraph contrast at the billion-to-one level in spectrally broad light, as required for the direct imaging of planetary systems orbiting the nearby stars. Here we explore design options for a physically realizable occulting mask composed of a metallic and a dielectric thin film, each profiled in thickness and superimposed on a glass substrate. We show that such hybrid masks, together with a deformable mirror for control of wavefront phase, offer contrast performance better than 10 -9 over spectral bandwidths up to 30% with Lyot coronagraph throughput efficiencies of 66% or more.