We present measurements of interstellar $H_2$ absorption lines in the continuum spectra of 54 early-type stars in the Galactic disk and halo and 3 stars in the Magellanic Clouds. The data were obtained with the Berkeley Extreme and Far-Ultraviolet Spectrometer (BEFS), part of the ORFEUS telescope, which flew on the ORFEUS-SPAS I and II space-shuttle missions in 1993 and 1996, respectively. The spectra extend from the interstellar cutoff at $912{AA}$ to about $1200{AA}$ with a spectral resolution of ${sim}3000$ and statistical signal-to-noise ratios between 10 and 65. Assuming a velocity profile derived from optical observations (when available), we model the column densities N(J) of the rotational levels J = 0 through 5 for each line of sight. Our data reproduce the relationships among molecular and total hydrogen column density, fractional molecular abundance, and reddening first seen in Copernicusobservations of nearby stars (Savage et al. 1977). The results show that most of these molecular clouds have $H_2$ total column densities between $10^{15}cm^{-2}$ and $10^{21}cm^{-2}$, and kinetic temperatures from 21 K to 232 K, with average of 89 K, consistent with the result of Copernicus (Savage et al. 1977).