The discrete-serpentine heterogeneous multi-arm space robot (DSHMASR) has more advantages than single discrete space robots or single serpentine space robots in complex tasks of on-orbit servicing. However, the mechanical structure complexity of the DSHMASR poses challenges for modeling and motion planning. In this paper, a coupled kinematic model and a coordinated trajectory planning method for the DSHMASR were proposed to address these issues. Firstly, an uncontrolled satellite and the DSHMASR were modeled based on the momentum conservation law. The generalized Jacobian matrix J_g of the space robotic system was derived. Secondly, the manipulation capability of the DSHMASR was analyzed based on the null-space of J_g. Furthermore, the cooperative capturing-monitoring trajectory planning method for DSHMASR was presented through the manipulability optimization. The expected trajectory of each arm’s tip can be obtained by pose deviations and velocity deviations between the tip and the target point. Additionally, the optimized joint velocities of each arm were calculated by combining differential kinematics and manipulability optimization. Therefore, the manipulability of DSHMASR in the direction of the capture operation was enhanced simultaneously as it approached the target satellite. Finally, the proposed algorithm was demonstrated by establishing the Adams–Simulink co-simulation model. Comparisons with traditional approaches further confirm the outperformance of the proposed method in terms of manipulation capability.