The Coulomb explosion of the hydrogen molecule, after absorption of a 76 eV photon, has been studied by momentum imaging the two electrons and the two protons. Absolute fully differential cross sections of high statistical quality are obtained. A subset of the overall data, namely, equal electron-energy sharing, is used to investigate the effects of molecular orientation on the photoelectron angular distribution. Departures from the first-order helium-like model are evident in detection geometries where electron-electron correlation is "frozen."