We propose and demonstrate a dual-band microwave photonic radar scheme based on a monolithic integrated mutual injection laser. Based on the photon-photon resonance (PPR) and the gain switching effect of the integrated laser, the C-/X-band triangular chirp signals with high-quality and comparable power at 4.75-5.25 GHz and 9.5-10.5 GHz are generated. In the current proof-of-concept experiment, the range resolution of the dual-band chirp signals can reach 16.9 cm, compared with the single-band chirp signal that cannot distinguish the targets. Through the application of a single integrated device and a transceiver module sharing a set of antennas, the dual-band microwave photonic radar system scheme improves the system integration.