Possible models of the arrangement of hydrogen atoms at the sites of the cubic lattice of titanium oxyhydride TiOyHp with vacancies in the metallic and nonmetallic sublattices are considered. It was found that titanium oxyhydride retains the B1 type crystal lattice of the initial cubic titanium monoxide TiOy and contains structural vacancies in the metal and oxygen sublattices. Comparison of the found analytical expressions for the intensity of diffraction reflections with experimental X-ray and neutron diffraction data showed that interstitial H atoms in oxyhydrides occupy vacant octahedral positions 4(b) of the oxygen sublattice. No displacement of H atoms in tetrahedral positions 8(c) is observed. A disorder-order phase transition channel associated with the formation of an ordered monoclinic titanium oxyhydride of the Ti5O5 type was found. The distribution functions of Ti, O, and H atoms in the partially ordered monoclinic oxyhydride Ti5.33O5.12H0.74 (Ti0.89O0.85H0.12) with a Ti5O5-type structure are calculated for the first time, and the concentrations of these atoms at the positions of its lattice were found.