We have performed a comprehensive ground-based observational program aimed at characterizing the circumstellar material orbiting three single white dwarf stars previously known to possess gaseous disks. Near-infrared imaging unambiguously detects excess infrared emission towards Ton 345 and allows us to refine models for the circumstellar dust around all three white dwarf stars. We find that each white dwarf hosts gaseous and dusty disks that are roughly spatially coincident, a result that is consistent with a scenario in which dusty and gaseous material has its origin in remnant parent bodies of the white dwarfs planetary systems. We briefly describe a new model for the gas disk heating mechanism in which the gaseous material behaves like a Z II region. In this Z II region, gas primarily composed of metals is photoionized by ultraviolet light and cools through optically thick allowed Ca II-line emission.