Gamma-ray burst (GRB) 111215A was bright at X-ray and radio frequencies, but not detected in the optical or near-infrared (nIR) down to deep limits. We have observed the GRB afterglow with the Westerbork Synthesis Radio Telescope and Arcminute Microkelvin Imager at radio frequencies, with the William Herschel Telescope and Nordic Optical Telescope in the nIR/optical, and with the Chandra X-ray Observatory. We have combined our data with the Swift X-Ray Telescope monitoring, and radio and millimeter observations from the literature to perform broadband modeling, and determined the macro- and microphysical parameters of the GRB blast wave. By combining the broadband modeling results with our nIR upper limits we have put constraints on the extinction in the host galaxy. This is consistent with the optical extinction we have derived from the excess X-ray absorption, and higher than in other dark bursts for which similar modeling work has been performed. We also present deep imaging of the host galaxy with the Keck I telescope, Spitzer Space Telescope, and Hubble Space Telescope (HST), which resulted in a well-constrained photometric redshift, giving credence to the tentative spectroscopic redshift we obtained with the Keck II telescope, and estimates for the stellar mass and star formation rate of the host. Finally, our high resolution HST images of the host galaxy show that the GRB afterglow position is offset from the brightest regions of the host galaxy, in contrast to studies of optically bright GRBs.