We present measurements of interstellar H2 absorption lines in the continuum spectra of seven early-type stars in the Galactic disk at distances between 1 and 4 kpc. 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 mean excitation temperatures and proton density limits for the H2 clouds along each line of sight. The gross properties of the H2-bearing clouds (e.g., column density, spatial density, cloud size) are consistent with those derived from Copernicus observations, though our lines of sight are much longer, with lower average reddenings and neutral gas densities. We find that the molecular fraction of the neutral hydrogen remains ~ 0.1 out to distances of 4 kpc in the Galactic disk.