The operation of an integrated two-dimensional complementary metal–oxide–semiconductor inverter with well-matched input/output voltages is reported. The circuit combines a few-layer MoS2 n-MOSFET and a black phosphorus (BP) p-MOSFET fabricated using a common local backgate electrode with thin (20 nm) HfO2 gate dielectric. The constituent devices have linear threshold voltages of −0.8 V and +0.8 V and produce peak transconductances of 16 μS μm−1 and 41 μS μm−1 for the MoS2 n-MOSFET and BP p-MOSFET, respectively. The inverter shows a voltage gain of 3.5 at a supply voltage, VDD = 2.5 V, and has peak switching current of 108 μA and off-state current of 8.4 μA (2.4 μA) at VIN = 0 (VIN = 2.5 V). In addition, the inverter has voltage gain greater than unity for VDD ≥ 0.5 V, has open butterfly curves for VDD ≥ 1 V, and achieves static noise margin over 500 mV at VDD = 2.5 V. The voltage gain was found to be insensitive to temperature between 270 and 340 K, and AC large and small-signal operation was demonstrated at frequencies up to 100 kHz. The demonstration of a complementary 2D inverter which operates in a symmetric voltage window suitable for driving a subsequent logic stage is a significant step forward in developing practical applications for devices based upon 2D materials.