To evaluate power system large-scale blackout risks under compound typhoon-rainstorm events, a risk assessment method that explicitly considers compound climate conditions is proposed. First, Bayesian model averaging (BMA) is employed to integrate multiple candidate marginal distributions. Combined with Copula functions, a robust wind-rain joint probability model for small samples is constructed. Constrained by the joint return period, a Gaussian mixture model (GMM) is further adopted to cluster and generate three representative compound climate scenarios. Second, a climate-sensitive multi-type source-load model is developed to characterize the coordinated responses of restricted wind-solar-hydro power outputs and meteorological load variations. Finally, a multi-dimensional blackout risk index system is formulated by integrating equipment vulnerability models with cascading failure simulations, incorporating outage consequences and annual occurrence probabilities. Simulation results show that the strong-wind scenario poses a significantly higher blackout risk than the other scenarios, while moderate-intensity but high-frequency events yield the highest annual expected risk, highlighting their long-term risk contribution. The proposed method effectively quantifies the differentiated compound-scenario risks and provides a quantitative basis for coastal power grid disaster prevention planning.