High-throughput dynamic imaging of cells and organelles is essential for understanding complex cellular responses. We report Mantis, a high-throughput 4D microscope that integrates two complementary, gentle, live-cell imaging technologies: remote-refocus label-free microscopy and oblique light-sheet fluorescence microscopy. Additionally, we report shrimPy, an open-source software for high-throughput imaging, deconvolution, and single-cell phenotyping of 4D data. Using Mantis and shrimPy, we achieved high-content correlative imaging of molecular dynamics and the physical architecture of 20 cell lines every 15 minutes over 7.5 hours. This platform also facilitated detailed measurements of the impacts of viral infection on the architecture of host cells and host proteins. The Mantis platform can enable high-throughput profiling of intracellular dynamics, long-term imaging and analysis of cellular responses to perturbations, and live-cell optical screens to dissect gene regulatory networks.