We present a cross-calibration of CO- and dust-based molecular gas masses at z<=0.2. Our results are based on a survey with the IRAM 30-m telescope collecting CO(1-0) measurements of 78 massive (logM*/M_{sun}_>10) galaxies with known gas-phase metallicities and with IR photometric coverage from Wide-field Infrared Survey Explorer(WISE; 22um) and Herschel Spectral and Photometric Imaging Receiver (SPIRE; 250, 350, 500um). We find a tight relation (~0.17dex scatter) between the gas masses inferred from CO and dust continuum emission, with a minor systematic offset of 0.05dex. The two methods can be brought into agreement by applying a metallicity-dependent adjustment factor (~0.13dex scatter). We illustrate that the observed offset is consistent with a scenario in which dust traces not only molecular gas but also part of the HI reservoir, residing in the H_2_-dominated region of the galaxy. Observations of the CO(2-1) to CO(1-0) line ratio for two-thirds of the sample indicate a narrow range in excitation properties, with a median ratio of luminosities <R_21_>~0.64. Finally, we find dynamical mass constraints from spectral line profile fitting to agree well with the anticipated mass budget enclosed within an effective radius, once all mass components (stars, gas, and dark matter) are accounted for.