Bound and free quantum resonances of molecular hydrogen exhibiting wave-function density at large internuclear separation, R ∼ 4-5 a.u., are excited via multi-step laser spectroscopy. Highly excited vibrational levels of H 2 are prepared via two-photon UV-photolysis of H 2 S. Subsequent twophoton Doppler-free precision measurements are performed connecting X 1 + g (v = 11) levels with F 1 + g outer-well levels. Detection and spectroscopic labelling of the quantum states is assisted by further laser excitation into the auto-ionisation continuum employing a third UV-laser. Level energies of high rotational states (J = 6, 7) in the outer-well state F 1 + g (v = 0) are accurately determined. The three-laser study demonstrates a method for probing resonances in the H 2 ionisation continuum with wave-function density at large internuclear separation R = 4-5 a.u., large angular momenta J, and energy range 131,100-133,000 cm −1 , a hitherto unexplored territory.