The partial substitution of Ca²⁺ for Sr²⁺ in La₂SrAl₂O₇ was performed. The structure of the solid solution La₂Sr_1-xCa_xAl₂O₇ (x≤0.5) consists in the regular intergrowth of double perovskite P₂ slabs with unit rocksalt RS slabs. As the main result of Rietveld structure calculations, Ca²⁺ is found to replace Sr²⁺ in the A₂ sites of the RS slabs (nine-fold CN); the random occupancy of the A₁ sites (12-fold CN) in the middle of the P₂ slabs by La³⁺ and Sr²⁺ remains nearly unchanged. The formation of the P₂-RS intergrowth of the solid solution is easier than that of La₂SrAl₂O₇ but its stability is progressively weakened when the amount of Ca²⁺ increases. This is the very likely consequence of the simultaneous presence of La³⁺ and Ca²⁺ in the RS slabs. The comparison of these ordering phenomena in the aluminates and the corresponding superconducting cuprates is taken into account.