The structured illumination (SI) architecture can be adopted in a digital holographic (DH) microscope to enhance the spatial resolution. In this paper, we propose and demonstrate a compact and simple SI method in a self-referencing common-path configuration of DH microscopy. The combination of SI pattern generated by a compact disk and common-path off-axis geometry formed by Fresnel biprism introduces a low-cost and highly stable system to image both amplitude and phase objects with a twofold improvement of the spatial resolution. Experimental results for the case of a standard test sample validate the predicted resolution enhancement compared to that of the conventional imager. The presented DH method allows for imaging living cells with more detail compared to the conventional DH microscopes.