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An unconventional “heteromorphic” superlattice (HSL) is realized, comprised of repeated layers of different materials with differing morphologies: semiconducting pc-In2O3 layers interleaved with insulating a-MoO3 layers. Originally proposed by Tsu in 1989, yet never fully realized, the high quality of the HSL heterostructure demonstrated here validates the intuition of Tsu, whereby the flexibility of the bond angle in the amorphous phase and the passivation effect of the oxide at interfacial bonds serve to create smooth, high-mobility interfaces. The alternating amorphous layers prevent strain accumulation in the polycrystalline layers while suppressing defect propagation across the HSL. For the HSL with 7:7 nm layer thickness, the observed electron mobility of 71 cm2/Vs, matches that of the highest quality In2O3 thin films. The atomic structure and electronic properties of crystalline In2O3 / amorphous MoO3 interfaces are verified using ab-initio molecular dynamics simulations and hybrid functional calculations. This work generalizes the superlattice concept to an entirely new paradigm of morphological combinations.