We present measurements of diffuse interstellar H2 absorption lines in the continuum spectra of 10 early-type stars. The data were observed with the Berkeley Extreme and Far-Ultraviolet Spectrometer (BEFS) of the ORFEUS telescope on board the ORFEUS-SPAS I and II space-shuttle missions in 1993 and 1996, respectively. The spectra extend from the interstellar cutoff at 912 Å to about 1200Åwith a resolution of ~ 3000 and statistical signal-to-noise ratios between 10 and 65. Adopting Doppler broadening velocities from high-resolution optical observations, we obtain the H2 column densities of rotational levels J00 = 0 through 5 for each line of sight. The kinetic temperatures derived from J" = 0 and 1 states show a small variation around the mean value of 80 K, except for the component toward HD 219188, which has a temperature of 211 K. Based on a synthetic interstellar cloud model described in our previous work, we derive the incident UV intensity IUV and the hydrogen density nH of the observed components to be -0.4 ≤ log IUV ≤ 2.2 and 6.3 ≤ nH ≤ 2500 cm-3, respectively.