Compute-in-memory (CIM) with emerging non-volatile memories (eNVMs) is time and energy efficient for deep neural network (DNN) inference. However, challenges still remain for DNN in-situ training with eNVMs due to the asymmetric weight update behavior, high programming latency and energy consumption. To overcome these challenges, a hybrid precision synapse combining eNVMs with capacitor has been proposed. It leverages the symmetric and fast weight update in the volatile capacitor, as well as the non-volatility and large dynamic range of the eNVMs. In this article, DNN in-situ training architecture with hybrid precision synapses is proposed and system level benchmarked is conducted. First, the circuit modules required for in-situ training with hybrid precision synapses are designed and the system architecture is proposed. Then, the impact of different weight precision configurations, weight transfer interval and limited capacitor retention time on training accuracy is investigated by incorporating hardware properties into Tensorflow simulation. Finally, the system-level benchmark is conducted at 32nm technology node in the modified NeuroSim simulator for hybrid precision synapse, in comparison with the baseline designs that are solely based on eNVMs or SRAM technology. The benchmark results show that CIM accelerator based on hybrid precision synapse achieves at least 3.07x and 2.89x better energy efficiency for training compared with its eNVM counterparts and SRAM technology at 32nm node, respectively. 227x and 33.8x better energy efficiency are obtained when compared to GPU and TPU. The scaling trend of hybrid precision synapse is projected towards 7nm node and comparison with state-of-the-art 7nm SRAM technology is made.