Due to the difference in output characteristics between the line-commutated converter-based high-voltage direct current (LCC-HVDC) and voltage-source converter-based high-voltage direct current (VSC-HVDC), the hybrid multi-infeed high-voltage direct current (HMIDC) presents complex coupling characteristics. As the AC side is disturbed, the commutation failure (CF) occurring on the LCC side is the main factor threatening the safe operation of the system. In this paper, the simplified equivalent network model of HMIDC is established by analyzing the output characteristics of VSC and LCC. Hereafter, based on the derived model and the control system of LCC-HVDC, the dynamic equations of the extinction angle are deduced. Consequently, by applying the phase portrait method, the causes of CF occurring in the HMIDC system as well as the impacts of control parameters on the transient stability are revealed. Furthermore, the stabilization boundaries for the reference value of the DC voltage are obtained via the above analysis. Finally, the theoretical analysis is verified by the simulations in the PSCAD/EMTDC.