The joint radar and communication (JRC) system providing both large-capacity transmission and high-resolution ranging will play a pivotal role in the next-generation wireless networks (e.g., 6G and beyond) and defense applications. Here, we propose and experimentally demonstrate a novel photonics-assisted millimeter-wave (mm-wave) JRC system with a multi-Gbit/s data rate for communication function and centimeter-level range resolution for radar function. The key is the design of the intermediate-frequency (IF) JRC signal through the angle modulation of the linear frequency modulation (LFM) radar carrier using orthogonal frequency division multiplexing (OFDM) communication signal, inspired by the idea of constant-envelope OFDM (CE-OFDM). This IF angle-modulated waveform facilitates the broadband photonic frequency (phase)-multiplying scheme to generate mm-wave JRC signal with multiplied instantaneous bandwidth and phase modulation index for high-resolution LFM radar and noise-robust CE-OFDM communication. It is with fixed low power-to-average power ratio to render robustness against the nonlinear distortions. In proof-of-concept experiments, a 60-GHz JRC signal with an instantaneous bandwidth over 10-GHz is synthesized through a CE-LFM-OFDM signal encoded with a 2-GBaud 16-QAM OFDM signal. Consequently, a 1.5-cm range resolution of two-dimension imaging and an 8-Gbit/s data rate are achieved for both radar and communication functions, respectively. Furthermore, the proposed JRC system is able to achieve higher radar range resolution and better anti-noise communication, when using higher-order photonic frequency multiplying.