Given that high uncertainty in rock slope stability is induced by the random spatial distribution of joints, and the discrete element method is restricted by low computational efficiency during large-sample probabilistic sampling, the joint dip direction, dip angle, cohesion, and internal friction angle of structural planes are adopted as random input variables in this research. The Phase2 finite element method is employed as the deterministic mechanical solver, and a random collocation space is constructed by coupling with Latin hypercube sampling. Based on the Hermite orthogonal polynomial expansion, an explicit stochastic response surface surrogate model for the factor of safety is established. By this means, the numerical convergence of large-scale calculations is safeguarded while the mechanical characterization of structural planes is simultaneously considered. According to the results, a significant geometric boundary control effect on slope stability is exerted by joint structural planes. A "V"-shaped evolution trend between the single joint dip angle and the factor of safety is observed, wherein persistent shear sliding is highly prone to be triggered at intermediate dip angles, whereas global instability is kinematically suppressed by steep and gentle dip angles. Moreover, a fitting accuracy of R2 = 0.96 is achieved by the constructed second-order explicit surrogate model with cross-terms. Under the premise that the computational overhead of the finite element method is significantly reduced, a relative error of only 1.2% in the failure probability is obtained. For the case slope, a negative reliability index (β = -0.43) is calculated, indicating that the mean anti-sliding state has already fallen into the failure domain. Consequently, the extremely high risk of instability under random parameter coupling is quantitatively revealed, and the rigor and practical value of the proposed computational framework in the reliability evaluation of rock masses with complex structural planes are thoroughly verified.