Integrating millimeter wave (mmWave)technology in both communication and sensing is promising as it enables the reuse of existing spectrum and infrastructure without draining resources. Most existing systems piggyback sensing onto conventional communication modes without fully exploiting the potential of integrated sensing and communication (ISAC) in mmWave radios (not full-fledged). In this paper, we design and implement a full-fledged mmWave ISAC system Gemini; it delivers raw channel states to serve a broad category of sensing applications. We first propose the mmWave self-interference cancellation approach to extract the weak reflected signals for near-field sensing purposes. Then, we develop a joint optimization scheduling framework that can be utilized in accurate radar sensing while maximizing the communication throughput. Finally, we design a united fusion sensing algorithm to offer a better sensing performance via combining monostatic and bistatic modes. We evaluate our system in extensive experiments to demonstrate Gemini's capability of simultaneously operating sensing and communication, enabling mmWave ISAC to perform better than the commercial off-the-shelf mmWave radar for 5G cellular networks.