We compare mid-infrared (mid-IR), extinction-corrected H alpha, and CO (2-1) emission at 70-160 pc resolution in the first four PHANGS-JWST targets. We report correlation strengths, intensity ratios, and power-law fits relating emission in JWST's F770W, F1000W, F1130W, and F2100W bands to CO and H alpha. At these scales, CO and H alpha each correlate strongly with mid-IR emission, and these correlations are each stronger than the one relating CO to H alpha emission. This reflects that mid-IR emission simultaneously acts as a dust column density tracer, leading to a good match with the molecular-gas-tracing CO, and as a heating tracer, leading to a good match with the H alpha. By combining mid-IR, CO, and H alpha at scales where the overall correlation between cold gas and star formation begins to break down, we are able to separate these two effects. We model the mid-IR above I ( nu ) = 0.5 MJy sr(-1) at F770W, a cut designed to select regions where the molecular gas dominates the interstellar medium (ISM) mass. This bright emission can be described to first order by a model that combines a CO-tracing component and an H alpha-tracing component. The best-fitting models imply that similar to 50% of the mid-IR flux arises from molecular gas heated by the diffuse interstellar radiation field, with the remaining similar to 50% associated with bright, dusty star-forming regions. We discuss differences between the F770W, F1000W, and F1130W bands and the continuum-dominated F2100W band and suggest next steps for using the mid-IR as an ISM tracer.