A series of aluminate-based oxyhydrides, Sr3-xAxAlO4H (A = Ca, Ba; x = 0, 1), has been synthesized by high-temperature reaction of oxide and hydride precursors under a H2 atmosphere. Their crystal structures determined via X-ray and neutron powder diffraction are isostructural with tetragonal Sr3AlO4F (space group I4/mcm), consisting of (Sr1-x/3Ax/3)2H layers and isolated AlO4 tetrahedra. Rietveld refinement based on the diffraction patterns and bond-valence-sum analysis show that Ba preferentially occupies the 10-coordinated Sr1 sites, while Ca strongly prefers to occupy the 8-coordinated Sr2 sites. Luminescence owing to the 4f-5d transition of Eu2+ or Ce3+ was observed from Eu- and Ce-doped samples, Sr3-x-yAxByAlO4H (A = Ca, Ba; B = Eu, Ce; x = 0, 1, y = 0.02), under excitation of near-ultraviolet light. Compared with its fluoride analogue, Sr3AlO4H:Ce3+ shows red shifts of both the excitation and emission bands, which is consistent with the reported hydride-based phosphors and can be explained by the covalency of the hydride ligands. The observed luminescence spectra can be decomposed into two sets of sub-bands corresponding to Ce3+ centers occupying Sr1 and Sr2 sites with distinctly different Stokes shifts (1.27 and 0.54 eV, respectively), as suggested by the results of constrained density functional theory (cDFT). The cDFT results also suggest that the large shift for Ce3+ at Sr1 is induced by large distortion of the coordinated structure with shortening of the H-Ce bond in the excited state. The current findings expand the class of oxyhydride materials and show the potential of hydride-based phosphors for optical applications.