This paper presents the theoretical design of an artificial dielectric exhibiting narrowband frequency selective properties in the bulk without relying on periodic placement of elements. In this manner, it initiates a novel approach that bypasses the drawbacks of the traditional frequency selective surfaces (FSS), namely, unwanted passbands, dependence on excitation angle and polarization, and difficulties in conversion from planar to curved geometries. The key design elements are the concentric geometry of the inclusions and the use of Lorentzian resonant media. A discussion of physical resonant materials is presented, substantiating the credibility of the theoretical design. To illustrate the approach, a novel complex medium is synthesized as an ensemble of spherical particles composed of a lossy core coated with a highly resonant dielectric layer and embedded into a dielectric host. The resulting structure is an amorphous substance, lossy over its entire spectrum except for two narrow-band transparency windows, where it may become as lossless as desired. The parameter space of the system is thoroughly analyzed which determines the type of constitutive materials and geometries for tailor-designing the windows according to specifications (shape, positioning and overall normalization). In this sense, the lossy concentric structure forms an ideal candidate for thin absorbing films (TAF's) with extensive applications in antenna systems, RF absorbers, and anechoic chambers.