We report a backgated InAs/GaSb double quantum well device grown on GaSb substrate. The use of the native substrate allows for high materials quality with electron mobility in excess of 500 000 cm2/Vs at sheet charge density of 8 × 1011 cm−2 and approaching 100 000 cm2/Vs near the charge neutrality point. Lattice matching between the quantum well structure and the substrate eliminates the need for a thick buffer, enabling large back gate capacitance and efficient coupling with the conduction channels in the quantum wells. As a result, quantum Hall effects are observed in both electron and hole regimes across the hybridization gap.