We present a unified treatment of the diffraction properties of stratified volume holographic optical elements (SVHOE's). We show that the relative phasing of the diffraction orders as they propagate from layer to layer gives rise to a unique notched diffraction response of the +1 order (for the case of Bragg incidence) as a function of the normalized buffer-layer thickness, the grating spatial frequency, and the readout wavelength. For certain combinations of these parameters Bragg diffraction behavior characteristic of volume holographic optical elements (VHOE's) is observed, whereas for other combinations pure Raman-Nath behavior periodically recurs. By using these same relative-phasing arguments, the principal features of the periodic angular sensitivity of the +1 and -1 orders can be predicted. In addition to examining the fundamental aspects of SVHOE diffraction behavior, we discuss several possible applications, including optical array generation, spatial frequency filtering, and wavelength notch filtering. With the use of the SVHOE concept, holographic materials with otherwise exemplary characteristics that are currently available only in thin-film form can be used in structures designed either to access unique SVHOE diffraction properties or to emulate conventional VHOE's.