The standard method for estimating the mass of the interstellar medium (ISM) in a galaxy is to use the 21 cm line to trace the atomic gas and the CO 1-0 line to trace the molecular gas. In this paper, we investigate the alternative technique of using the continuum dust emission to estimate the mass of gas in all phases of the ISM. Using Herschel observations of 10 galaxies from the Herschel Reference Survey and the Herschel Virgo Cluster Survey, we show that the emission detected by Herschel is mostly from dust that has a temperature and emissivity index similar to that of dust in the local ISM in our galaxy, with the temperature generally increasing toward the center of each galaxy. We calibrate the dust method using the CO and 21 cm observations to provide an independent estimate of the mass of hydrogen in each galaxy, solving the problem of the uncertain "X-factor" for the CO observations by minimizing the dispersion in the ratio of the masses estimated using the two methods. With the calibration for the dust method and the estimate of the X-factor produced in this way, the dispersion in the ratio of the two gas masses is 25%. The calibration we obtain for the dust method is similar to those obtained from Herschel observations of M31 and from Planck observations of the Milky Way. We discuss the practical problems in using this method. © 2012. The American Astronomical Society. All rights reserved..