Here we investigate stripes of alternating structural phases spontaneously forming in epitaxially strained Ca₂RuO₄ thin films below the metal-insulator transition. Using large-volume X-ray reciprocal-space mapping, we show that satellite-pattern intensities across 24 symmetry-inequivalent Bragg reflections collapse onto a single parameter-free curve. The collapse identifies a coherent martensitic laminate of few-nm-wide domains separated by 012 interfaces, with displacements along ⟨012̄⟩. Satellite-extinction analysis demonstrates that both coexisting phases retain the bulk orthorhombic space group despite the pseudocubic LaAlO₃ substrate, biaxial epitaxial strain, and intrinsic strain at the interfaces. Classical invariant-plane-strain crystallography thus governs the nanoscale domain geometry of a Mott insulator with intertwined magnetic, electronic, and lattice order.