  The ionization energy of ortho-H$_2$ has been determined to be
$E^\mathrm{o}_\mathrm{I}(\mathrm{H}_2)/(hc)=124\,357.238\,062(25)$ cm$^{-1}$
from measurements of the GK(1,1)--X(0,1) interval by Doppler-free two-photon
spectroscopy using a narrow band 179-nm laser source and the ionization energy
of the GK(1,1) state by continuous-wave near-infrared laser spectroscopy.
$E^\mathrm{o}_\mathrm{I}$(H$_2$) was used to derive the dissociation energy of
H$_2$, $D^{N=1}_{0}$(H$_2$), at $35\,999.582\,894(25)$ cm$^{-1}$ with a
precision that is more than one order of magnitude better than all previous
results. The new result challenges calculations of this quantity and represents
a benchmark value for future relativistic and QED calculations of molecular
energies.
