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The alkaline earth stannate BaSnO3 is a semiconductor with high carrier mobility at room-temperature when doped with La3+. When a thin epitaxial layer of LaInO3 is grown on lightly doped BaSnO3, a polar discontinuity between the orthorhombic, polar LaInO3 and the cubic, nonpolar Ba0.998La0.002SnO3 leads to an electronic reconstruction, where LaInO3 remotely dopes Ba0.998La0.002SnO3, creating carriers for high mobility devices. We determine aspects of the crystalline structure of the LaInO3/BaSnO3 film that affect the polar discontinuity using synchrotron x-ray diffraction. Specifically, we examine the role of oxygen octahedral rotations and anti-parallel cation displacements in influencing the polarization of the LaInO3/BaSnO3 interface. These structural distortions are characterized by measuring half-order Bragg peaks of thin film LaInO3/BaSnO3/SrTiO3 heterostructures grown by pulsed laser deposition. We find that for films as thin as 3 unit cells, epitaxial LaInO3 has 2 distinct domains, one with the same Glazer tilt pattern as that of bulk LaInO3, a+b−b−, and a second rotated 90° in-plane from the first and having tilt pattern b−a+b−. Additionally, we observe a sudden and large increase in cation displacements along the [011] and [101] directions across the LaInO3/BaSnO3 interface due to the strength of the octahedral rotations.