This paper constructs a synthetic framework for the operational reliability evaluation and risk mitigation of asynchronous grids coupled through flexible high-voltage DC (HVDC) systems (AGs-FDCSs). First of all, an analytical model for the unavailability of DC units is reformulated to refine and facilitate the reliability modeling of such flexible HVDC systems considering their time-dependent features as well as the impacts of converter station configurations. Subsequently, the operational risk associated with the redispatch procedure is extended to the reliability evaluation of composite power system, and the risk is mitigated through an optimal power flow (OPF) based short-term state assessment model. In addition, some new reliability indices like expected DC transmission power (EDCTP) and DC terminal outage probability (DCTOP) are defined to quantify the impact of the reliability of flexible HVDC systems on the entire grid. The effectiveness of the proposed framework on a modified IEEE RTS-79 system is validated with the elaborate discussions on the time-dependent reliability of AGs-FDCSs as well as the impacts of the converter station configurations.