The spectrum of the 5g-4f inter-Rydberg band of H-2 has been recorded with a difference frequency laser system and analyzed using multichannel quantum defect theory (MQDT). New transitions have been observed; in addition to the singlet-triplet splittings previously observed, the hyperfine structure of the ortho-hydrogen spectrum is partially resolved in the present experiment. MQDT is used to analyze the data in a two stage process. First, the ab initio MQDT predictions were refined by fitting the quantum defect functions over a range of internuclear separation R. Second, 4f singlet and triplet quantum defects are extracted from the para-hydrogen spectra, i.e., those lines without complicating hyperfine structure. This information was then used to calculate the fine structure of a sample ortho-hydrogen line, R-3(2)v(+)=0. While the spectra are predominantly composed of absorption lines, some transitions from high vibrational levels of the 5g triplet manifold to 4f triplet levels are observed in stimulated emission.