We consider the spectral properties of dielectric waveguides with low refractive index cores and binary layered claddings, such as Bragg fibers and integrated-ARROWs. We show that the full, nontrivial, 2-D spectrum of Bloch bands (hence bandgaps) of such claddings correspond, in structure and topology, to the dispersion properties of both constituent layer types; quantitatively demonstrating an intimate relationship between the bandgap and antiresonance guidance mechanisms. The dispersion functions of these layers, and the interactions thereof, thus form what we coin the Stratified Planar Anti-Resonant Reflecting OpticalWaveguide (SPARROW) model, capable of quantitative, analytic, descriptions of many nontrivial bandgap and antiresonance properties. The SPARROW model is useful for the spectral analysis and design of Bragg fibers and integrated-ARROWs with cores of arbitrary refractive index (equal to or less than the lowest cladding index). Both waveguide types are of interest for sensing and microfluidic applications due to their natural ability to guide light within low-index cores, permitting low-loss guidance within a large range of gases and liquids. A liquid-core Bragg fiber is discussed as an example, demonstrating the applicability of the SPARROW model to realistic and important waveguide designs.