The series line-commutated converter (LCC) and modular multilevel converter (MMC) hybrid high-voltage direct current (HVDC) system provides a more economical and flexible alternative for ultra-HVDC (UHVDC) transmission, which is the so-called Baihetan-Jiangsu HVDC (BJ-HVDC) project of China. In one LCC and two MMCs (1+2) operation mode, the sub-module (SM) capacitors suffer the most rigorous overvoltage induced by three-phase-to-ground fault at grid-side MMC and valve-side single-phase-to-ground fault in internal MMC. In order to suppress such huge overvoltage, this paper demonstrates a novel alternative by employing the MMC-based embedded battery energy storage system (MMC-BESS). Firstly, the inducements of SM overvoltage are analyzed. Then, coordinated with MMC-BESS, new fault ride-through (FRT) strategies are proposed to suppress the overvoltage and improve the FRT capability. Finally, several simulation scenarios are carried out on PSCAD/EMTDC. The overvoltage suppression is verified against auxiliary device used in the BJ-HVDC project in a monopolar BJ-HVDC system. Further, the proposed FRT strategies are validated in the southern Jiangsu power grid of China based on the planning data in the summer of 2025. Simulation results show that the MMC-BESS and proposed FRT strategies could effectively suppress the overvoltage and improve the FRT capability.