Holography enables intriguing microscopic imaging modalities, particularly through Quantitative Phase Imaging (QPI), which utilizes the phase of coherent light as a way to reveal the contrast in transparent and thin microscopic specimens. Despite the limitation of image sensors, which detect only light intensity, phase information can still be recorded within a two-dimensional interference pattern between two distinct light waves. Numerical reconstruction is later needed to retrieve the amplitude and phase from such holographic measurements. To this end, we introduce HoloADMM, a novel interpretable, learning-based approach for in-line holographic image reconstruction. HoloADMM enhances imaging capability with spatial image super-resolution, offering a versatile framework that accommodates multiple illumination wavelengths and supports extensive refocusing ranges with up to 10 um precision. Our results indicate a substantial improvement in reconstruction quality over existing methods and demonstrate HoloADMM's effective adaptation to real holographic data captured by our Digital in-line Holographic Microscope (DIHM). This work not only advances holographic imaging techniques but also broadens the potential for non-invasive microscopic analysis applications.