Synchronous movements of the entire face, from chewing to grimacing, offer significant insights into internal physiological processes. Mice, with discernible facial responses and evolutionarily conserved mammalian facial movement control circuits, provide an ideal model to unravel the link between facial movement and internal physiological states in mammals. However, existing frameworks lack the spatial or temporal resolution to track motion of the entire mouse face, due to its small and conical form factor. We introduce Cheese3D, a computer vision system that first captures high-speed 3D motion of the entire mouse face (including ears, eyes, whisker pad, jaw, while covering both sides of the face) using a calibrated six-camera array. The interpretable framework extracts dynamics of anatomically-meaningful 3D facial features in absolute world units at sub-millimeter precision. The precise face-wide motion data generated by Cheese3D provides clear physiological insights, as shown by proof-of-principle experiments predicting time under anesthetic from subtle facial patterns, and inferring tooth and muscle anatomy from fast chewing motions. Cheese3D can serve as a discovery tool that renders facial movements highly interpretable as a readout of otherwise hidden internal states.