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• The mode-decoupling capability of the HIIRS was analyzed and validated. • The damping range and the coupling effects between the damping and the stiffness of the HIIRS were investigated. • A piecewise-linearizing method was proposed to model the accumulator and thus to determine the analytical solution of the roll and pitch stiffness of the HIIRS. • The HIIRS could reduce the roll angle and pitch angle by 34.42% and 28.91%, while harvesting power as 87.69 W and 147.86 W, respectively. An innovative hydraulic integrated interconnected regenerative suspension system (HIIRS), which can simultaneously harvest suspension vibration energy and enhance the vehicle handling performance, is studied in this paper. One big challenge for the HIIRS is the mode-decoupling problem among the four vehicle vibration modes, namely bounce, roll, pitch, and warp modes. This paper comprehensively studied why and how the HIIRS could decouple the four modes. Specifically, the nonlinear fluidic model of the HIIRS was built and integrated with a 14DOF nonlinear vehicle model. Based on the model, the damping range and the coupling effects between the damping and the stiffness of the HIIRS were investigated. The roll and pitch stiffness of the HIIRS were calculated, where a novel piecewise-linearizing method was proposed to determine the analytic expression of the stiffness. Numerical experiments were conducted to demonstrate the mode-decoupling capability of the HIIRS and the influence of its parameters on the vehicle dynamics and the energy harvesting performances. In addition, the anti-roll, anti-pitch, and energy harvesting performances of the HIIRS were also studied and compared with a conventional off-road vehicle. The roll angle in a double lance change scenario and the pitch angle in a straight-line braking scenario could be respectively reduced by 34.42% and 28.91% when the initial system pressure in the HIIRS was 40 bar and the load resistance was 10 Ω. The corresponding regenerative power was 87.69 W and 147.86 W for the two cases. [ABSTRACT FROM AUTHOR]