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 49 different 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 [021]. 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.