The far-ultraviolet spectra of HD 219188, HD 94473, and HD 18100, three early-type stars in the Galactic halo, were obtained with the echelle spectrometer on the ORFEUS II telescope in 1996 November. We derive H(2) column densities for the rotational levels up to J " = 6 and estimate excitation temperatures and H(2) dissociation rates for the clouds toward HD 219188 and HD 94473. The results indicate that strong radiation fields might exist near these clouds, but these radiation fields do not seem to act as major heating sources. No significant H(2) absorption is seen toward HD 18100. The correlation between our H(2) column densities and published extinction maps confirms that the molecular clouds are associated with dust clouds that lie between the observed stars and the Sun. We estimate the conversion factor between N(H(2)) and W((12)CO) to be X(CO) = 4 +/- 2 x 10(19) cm(-2) (K km s(-1))(-1) for the clouds along the line of sight to HD 94473, consistent with previous estimates to within a factor of a few.