Despite the availability of multiple decades of passive microwave measurements from satellite platforms, their utility for developing quantitative, spatially distributed estimates of snowpack is yet to be realized. A major bottleneck is the use of simple conceptual retrieval model formulations that are ineffective in representing the significant heterogeneity and complexity of snow evolution, particularly over areas with complex topography and forest regions. Here we demonstrate a physics-constrained and interpretable Convolutional Neural Network (CNN) to learn the functional relationship utilizing multi-channel passive microwave brightness temperature measurements from the Advanced Microwave Scanning Radiometer 2 (AMSR2) and in-situ snow depth observations. The machine learning approach with CNN generates vastly improved snow depth estimates relative to the standard AMSR2 estimates. Compared to independent in-situ measurements of snow depth over the Continental United States, the domain averaged Pearson correlation measure is three times higher than that of the standard AMSR2 estimates (R²: 0.68 versus 0.21), while the systematic errors are reduced by approximately fourfold. Further, the CNN-based snow depth estimates also exhibit notable enhancements in regions with forests, deep snow, and melting snow, thereby alleviating the limitations faced by traditional algorithms in retrieving accurate snow depths. The interpretation of the CNN framework further indicates that the machine learning approach dynamically leverages both volume scattering and emission components from a suite of measured passive microwave signals to generate more accurate snow depth retrievals. The results of this study provide an important benchmark of high-quality snow retrievals from passive microwave satellite measurements by maximizing their information content.