A millimeter-wave (MMW) joint radar-communication (JRC) system with super-resolution is proposed and experimentally demonstrated, using optical heterodyne upconversion and self-coherent detection downconversion techniques. The point lies in the designed coherent dual-band constant envelope linear frequency modulation-orthogonal frequency division multiplexing (LFM-OFDM) signal with opposite phase modulation indexes for the JRC system. Then the self-coherent detection, as a simple and low-cost means, is accordingly facilitated for both de-chirping of MMW radar and frequency downconversion reception of MMW communication, which circumvents costly high-speed mixers along with MMW local oscillators and, more significantly, achieves the real-time decomposition of radar and communication information. Furthermore, a super-resolution radar range profile is realized through the coherent fusion processing of dual-band JRC signals. In experiments, a dual-band LFM-OFDM JRC signal centered at 54 GHz and 61 GHz is generated. The two bands feature an identical instantaneous bandwidth of 2 GHz and carry an OFDM signal of 1 Gbaud, which helps to achieve a 6-Gbit/s data rate for communication and a 1.76-cm range resolution for radar.