The effect of growth parameters in metalorganic chemical vapor deposition (MOCVD) on the crystal quality and surface morphology of the InAs/GaSb superlattices (SLs) on InAs substrates was systematically investigated by X-ray diffraction, scanning transmission electron microscopy, atomic force microscopy and photoluminescence. It was found that InAs/GaSb SLs grown at 530 degrees C with intentionally-formed GaAs-type interfaces exhibited lattice mismatch as low as -0.01%, abrupt SL interfaces and atomically smooth surface with a root mean square roughness of only 0.136 nm. Clear photoluminescence was observed around 8 mu m at 77 K for a long-wavelength SL structure. The nominal thickness of the GaAs-type interfacial layers and the overall SL strain can be effectively controlled by tuning the AsH3 flow rate. In addition, high-quality GaAs/GaSb SLs on InAs substrate were demonstrated as a replacement of the GaAsSb alloys. An AsH3-purge step was introduced after GaSb growth to form GaAs layers via As-Sb exchange. An optimal condition has resulted in lattice-mismatch of 0.21% and surface roughness of 0.122 nm for the GaAs/GaSb SLs.