We report a depth-extended, high-resolution fluorescence microscopy system based on interfering Bessel beams generated with double-ring phase (DRiP) modulation. The DRiP method effectively suppresses the Bessel side lobes, exhibiting a high resolution of the main lobe throughout a four- to five-fold improved depth of focus (DOF), compared to conventional wide-field microscopy. We showed both theoretically and experimentally the generation and propagation of a DRiP point-spread function (DRiP-PSF) of the imaging system. We further developed an approach for creating an axially-uniform DRiP-PSF and successfully demonstrated diffraction-limited, depth-extended imaging of cellular structures. We expect the DRiP method to contribute to the fast-developing field of non-diffracting-beam-enabled optical microscopy and be useful for various types of imaging modalities.