This study is concerned with a generalized version of the reliable capacitated facility location problem that guarantees a minimum level of service level in terms of satisfied demands under correlated facility disruptions with uncertain joint distribution. A linear mixed integer formulation for the generalized problem is presented and shown to correspond with the worst-case (distributionally robust) problem when the service-level function is submodular on the disruption scenarios. Managerial insights, including the effect of service-level parameters on optimal solutions, are presented based on experimental results. It is concluded that the proposed model may be used to design supply chain networks with the same expected total cost than the traditional reliable capacitated facility location problem, but with an improved total expected service level.