In this study, a copula-based stochastic fuzzy-credibility programming (CSFP) method is developed for planning regional-scale electric power systems (REPS). CSFP cannot only deal with multiple uncertainties presented as random variables, fuzzy sets, interval values as well as their combinations, but also reflect uncertain interactions among multiple random variables owning different probability distributions and having previously unknown correlations. Then, a CSFP-REPS model is formulated for planning the electric power systems (EPS) of the Jing-Jin-Ji region, where multiple scenarios with different joint and individual probabilities as well as different credibility levels are examined. Results reveal that electricity shortage would offset [4.8, 5.2]% and system cost would reduce [3.2, 3.3]% under synergistic effect scheme. Results also disclose that the study region's future electricity-supply pattern would tend to the transition to renewable energies and the share of renewable energies would increase approximately 10% over the planning horizon. Compared to the conventional stochastic programming, the developed CSFP method can more effectively analyze individual and interactive effects of multiple random variables, so that the loss of uncertain information can be mitigated and the robustness of solution can be enhanced. Moreover, based on the main effect analysis and regression analysis, CSFP-REPS can provide multiple joint planning strategies in a cost- and computation-effective way. Findings are useful for reflecting interactions among multiple random variables and disclosing their joint effects on modeling outputs of REPS planning problems.