In this thesis we study the diffuse molecular gas in the high-latitude cloud MBM 53 and the Southern Galactic Hemisphere. In particular, we conduct searches for dark molecular gas using high-sensitivity, high-velocity resolution CO(1-0) measurements, the OH 18 cm main lines, and composite radio and infrared dust spectra in a portion of the diffuse molecular cloud MBM 53. The results of our sensitive CO(1-0) observations increase the amount of CO-detectable molecular gas in MBM 53 by a factor of two with 15 new detections along 88 lines of sight. Our OH measurements find dark gas in 11 of 44 lines of sight overlapping the CO-sampled region. The CO(1-0) detections have AV threshold of 0.25 mag while the OH detection threshold in AV is 0.35 mag. In the composite radio-infrared spectra we found no indications of changes in dust grain size distribution or composition for the lines of sight where we had CO or OH detections compared to nondetections. Overall, we find that CO detections provide better information as to the extent of the borders of MBM 53 but OH detections provide a greater dark gas mass estimate.Finally, we examine the molecular content of a 2200 square degree region in Pegasus- Pisces with an estimated dark molecular gas fraction of 59%. Using data from the CO(1-0) Southern Galactic hemisphere, high-latitude survey by Magnani et al. (2000) we re-examinedthe CO-detectable mass estimates for the region. By averaging all the CO spectra in subsec- tions of varying sizes we decreased the rms of the averaged CO spectra by factors of 3-10, trading spatial resolution for sensitivity. With the new spectra we are able to make mass estimates as a function of sensitivity. Using the optimal estimate, the CO-detectable mass increases from 2200 to 4000 M, thereby decreasing the dark molecular gas fraction in the region to 0.24. In summary, sensitive CO(1-0) and OH 18 cm observations can detect signif- icantly more molecular gas than is revealed by conventional molecular mapping. Thus the dark gas content of molecular clouds is critically dependent on the sensitivity and velocity resolution of the corresponding CO and OH maps.