We present H-band light curves of Milky Way classical Cepheids observed as part of the Dark Energy, H_0_, and peculiar Velocities using Infrared Light from Supernovae survey with the Wide-Field Infrared Camera on the United Kingdom Infrared Telescope. Due to the crowded nature of these fields caused by defocusing the Camera, we performed difference-imaging photometry by modifying a pipeline originally developed to analyze images from the Transiting Exoplanet Survey Satellite. We achieved a photometric precision in line with expectations from photon statistics, reaching 0.01mag for 8<~H<~11mag. We used the resulting Cepheid light curves to derive corrections to "mean light" for random-phase Hubble Space Telescope observations in F160W. We find good agreement with previous phase corrections based on VI light curves from the literature, with a mean difference of -1+/-6mmag.