Current 3D localization microscopy approaches are fundamentally limited in their ability to image thick, densely labeled specimens. Here, we introduce a hybrid optical-electronic computing approach that jointly optimizes an optical encoder (a set of multiple, simultaneously imaged 3D point spread functions) and an electronic decoder (a neural-network-based localization algorithm) to optimize 3D localization performance under these conditions. With extensive simulations and biological experiments, we demonstrate that our deep-learning-based microscope achieves significantly higher 3D localization accuracy than existing approaches, especially in challenging scenarios with high molecular density over large depth ranges.