Sub-Doppler spectroscopy in alkali-metal vapor cells using two counterpropagating dual-frequency laser beams allows the detection of high-contrast sign-reversed natural-linewidth sub-Doppler resonances. Previously, a qualitative theory based on a simplified \ensuremath{\Lambda}-scheme model has been reported to explain underlying physics of this phenomenon. In this paper, an extended theoretical model of dual-frequency sub-Doppler spectroscopy (DFSDS) for the Cs
D1 line is reported. Taking into account the real atomic energy structure, main relaxation processes, and various nonlinear effects, this model describes quantitatively the respective contributions of involved physical processes and predicts main properties (height and linewidth) of the sub-Doppler resonances. Experimental tests are performed with a Cs vapor microfabricated cell and results are found to be in correct agreement with theoretical predictions. Spatial oscillations of the sub-Doppler resonance amplitude with translation of the reflection mirror are highlighted. A beat note between two laser systems, including one stabilized with DFSDS on a Cs vapor microcell, yields a fractional frequency stability of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ until 10-s averaging time. These results demonstrate that DFSDS could be an interesting approach for the development of a high-performance microcell-based optical frequency reference, with applications in various compact quantum devices.