Double-resonance laser spectroscopy via the state was used to probe the energy region below the third dissociation limit of molecular hydrogen. Resonantly enhanced multi-photon ionization spectra were recorded by detecting ion production as a function of energy using a time-of-flight mass spectrometer. Energies and line widths for the v = 14–17 levels of the state of H2 are reported and compared to experimental data obtained by using VUV synchrotron light excitation (Dickenson et al 2010 J. Chem. Phys. 133 144317) and fully ab initio non-adiabatic calculations of state energies and line widths (Glass-Maujean et al 2012 Phys. Rev. A 86 052507). Several high vibrational levels of the state were also observed in this region. Term energies and rotational constants for the v = 67–69 vibrational levels are reported and compared to highly accurate ro-vibrational energy level predictions from fully ab initio non-adiabatic calculations of the first six levels of H2 (Wolniewicz et al 2006 J. Mol. Spectrosc. 238 118). While additional observed transitions can be assigned to other states, several unassigned features in the spectra highlight the need for a fully integrated theoretical treatment of dissociation and ionization to understand the complex pattern of highly vibrationally excited states expected in this region.