Iron clusters react sequentially with hydrogen molecules to form multiply hydrogenated products. The increases in cluster ionization potential upon reaction verify that hydrogen chemisorbs dissociatively to form iron cluster-hydride complexes, FenHm. At low source temperatures, the cluster-hydride complexes take up additional hydrogen molecules which are shown to be physisorbed onto the underlying FenHm complexes to form FenHm(H2)p species. The infrared spectra of FenHm and FenDm (n=9-20) were obtained by the photodissociation action spectroscopic method in which depletion of the FenHm(H2)p and FenDm(D2)p species was the signature of absorption. The spectra, recorded in the 885-1090cm-1 region, consist of several overlapping bands, each approximately 20cm-1 in width. The dissimilarity of each FenHm(H2)p spectrum with the corresponding FenDm(D2)p spectrum indicates that the carrier involves hydrogen and is not merely due to absorption by the underlying iron cluster. Density functional calculations were performed on model complexes, Fe13H14 and Fe13D14, the iron portion of which was assumed to have Th symmetry. The infrared-active vibrational frequencies involving hydrogen bending and deuterium stretching are predicted to lie within the experimental frequency range of the experiment, well removed from the skeletal modes of the underlying iron cluster. The complexity of the observed spectra as compared to simulations based on the assumed (high-symmetry) model imply that the experimentally produced complexes possess low symmetry.