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To satisfy the requirements of accurate operational risk assessment of integrated transmission and distribution networks (I-T&D), an integrated operational risk assessment (I-ORA) algorithm is proposed. Specific cases demonstrate that I-ORA is necessary because it provides accurate handling of the coupling between transmission and distribution networks, accurate analysis of power supply mode (PSM) changes of important users and helps to improve security and stability of power grid operation. Two key technical requirements in the I-ORA algorithm are realized, integrated topology analysis and integrated power flow calculation. Under a certain contingency, integrated topology analysis is used to assess risks of substation power cut, network split and PSM changes of important users, while the integrated power flow calculation, based on the self-adaptive Leven-burg-Marquard method and Newton method, can be implemented to assess risks of heavy load/overload and voltage deviation. Besides, graphics processing unit is used to parallelly process some computation-intensive steps. Numerical experiments show that the proposed I-ORA algorithm can realize accurate assessment for the entire I-T&D. In addition, the efficiency and convergence are satisfying, which indicates that the proposed I-ORA algorithm can significantly benefit real practice in the coordination operation of I-T&D in the future.