The work is necessitated by search for new materials to detect ionizing radiation. The rare-earth doped ternary alkali earth-halide systems are promising scintillators showing high efficiency and energy resolution. Some aspects of crystal growth and data on the structural and luminescence properties of BaBrI and BaClI doped with low concentrations of Eu2+ ions are reported. The crystals are grown by the vertical Bridgman method in sealed quartz ampoule. New crystallographic data for BaClI single crystal obtained by single crystal X-ray diffraction are presented. Emission, excitation and optical absorption spectra as well as luminescence decay kinetics are studied under excitation by X-ray, vacuum ultraviolet and ultraviolet radiation. The energies of first 4f-5d transition in Eu2+ and band gaps of the crystals are obtained. The electronic band structure of the crystals are calculated using density functional theory as implemented in Vienna Ab initio Simulation Package. Calculated band gap energies are in accordance with the experimental estimates. The energy gaps between the valence band maximum and occupied Eu2+ 4f levels in BaBrI and BaClI are suggested. In addition, vacuum referred binding energy diagram of lanthanide levels is constructed using the chemical shift model.