The near-threshold highly bound states of all three stable isotopic variants of molecular hydrogen have been studied.Numerous perturbations and unexpected transitions are observed as far as 1cm-1 just below the second dissociation threshold. This complex structure may arise from a combination of nonadiabatic coupling between B, B′, C electronic states, perturbations due to fine and hyperfine interactions, and strong shape resonances. The perturbed near-threshold states and vibrational continuum exhibit finegrained structure, differing greatly between isotopes because of varying nonadiabatic coupling.