Reaction between Sr2Mn0.5Ir0.5O4 and CaH2 or LiH yields the iridium-containing oxyhydride phases Sr2Mn0.5Ir0.5O3.25H0.75 or Sr2Mn0.5Ir0.5O2.66H1.33, respectively. Analysis of Mn K-edge XANES data indicate the presence of Ir3+ centers in these oxyhydride phases, whose low-spin d6 configuration is consistent with the "covalent stabilization" of the metastable oxyhydride phases, as seen previously in analogous ruthenium and rhodium containing materials. Neutron powder diffraction data indicate the hydride ions are located exclusively within the "equatorial" anion sites of Sr2Mn0.5Ir0.5O3.25H0.75. In contrast, hydride ions are observed on both the equatorial and axial anion sites of Sr2Mn0.5Ir0.5O2.66H1.33. This highly unusual anion distribution is attributed to a combination of the strong trans-influence of Ir-H σ-bonds and the stabilization of fac-IrO3H3 centers by spin-orbit coupling effects. Magnetization data indicate that Sr2Mn0.5Ir0.5O4 and Sr2Mn0.5Ir0.5O3.25H0.75 adopt spin glass states at low temperature, behavior which is attributable to the cation disorder in Sr2Mn0.5Ir0.5O4 and the cation and anion disorder in Sr2Mn0.5Ir0.5O3.25H0.75. In contrast, magnetization data collected from Sr2Mn0.5Ir0.5O2.66H1.33 show no evidence of any magnetic phase transition down to 5 K, consistent with the dilution of the magnetic network by the introduction of diamagnetic Ir3+ on the formation of the oxyhydride phase.