Mismatched epitaxial layers of InxGa1-xAs and InyAl1-yAs were grown on InP by molecular beam epitaxy. Samples were characterized by high‐resolution x‐ray diffraction to assess layer quality as well as composition and strain. Measurement of epitaxial layer peak width is shown to be a sensitive, nondestructive means to judge the structural quality of a strained heterostructure. We find that for lattice mismatch of ±1% or less, the crystalline quality of epitaxial layers of InGaAs and InAlAs consistently remains high to thicknesses up to 3–9 times the Matthews–Blakeslee [J. Cryst. Growth 27, 118 (1974)] critical layer thickness. The findings are applied to the design and growth of high‐performance mismatched InAlAs/InGaAs/InP heterostructure field‐effect transistors.