We present measurements of interstellar H-2 absorption lines in the continuum spectra of seven early-type stars in the Galactic disk at distances between 1 and 4 kpc. Five of these stars provide lines of sight through the Sagittarius spiral arm. The spectra, obtained with the Berkeley EUV/FUV spectrometer on the ORFEUS telescope in 1993 September, have a resolution of 3000 and statistical signal-to-noise ratios between 20 and 80. We determine column densities for each observed rotational level and derive excitation temperatures and densities for the H-2 clouds along each line of sight. Our data continue the relationships among H-2 column density, fractional molecular abundance, and reddening apparent in Copernicus observations of nearby stars, indicating a common mechanism for H-2 production. Estimates of cloud temperatures and densities are consistent with those derived from Copernicus data. The molecular fraction f is nearly constant over a wide range of distances and mean reddenings, consistent with a model in which a significant fraction of the neutral ISM is associated with H-2-bearing molecular clouds, even along low-density lines of sight.