A cost-effective millimeter-wave (MMW) joint radar-communication (JRC) system with super resolution is proposed and experimentally demonstrated, using optical heterodyne up-conversion and self-coherent detection down-conversion 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 down-conversion reception of MMW communication, which circumvents the 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 signal. In experiments, a dual-band LFM-OFDM JRC signal centered at 54-GHz and 61-GHz is generated. The dual bands are featured with an identical instantaneous bandwidth of 2 GHz and carry an OFDM signal of 1 GBaud, which help to achieve a 6-Gbit/s data rate for communication and a 1.76-cm range resolution for radar.