Phased mission systems (PMS) are widely applied across diverse industrial systems. Technological advancements in these systems have markedly improved their performance. However, fault characteristics such as uncertainty and common cause failure (CCF) frequently emerge during failures, which significantly raises new challenges in reliability analysis. A novel system reliability analysis framework is proposed to address the mixed uncertainty and CCF in PMS. Specifically, a hybrid modeling approach that combines dynamic fault trees and generalized stochastic Petri nets (GSPN) is employed to accurately model PMS containing CCF. This approach integrates predicates and assertions from GSPN to define four reusable sub-Petri net models at different hierarchical levels, including module, phase, CCF, and overall mission levels. Furthermore, interval theory is incorporated into the framework to manage imprecise component lifetime data. For uncertainty quantification, a synergistic approach combining genetic algorithm and Monte Carlo simulation is utilized. Additionally, a simplified approach is introduced to reduce the complexity of computing the reliability boundary values of PMS. Finally, the proposed method is applied to conduct reliability analysis of a phased altitude and orbit control system. The analysis results validate its effectiveness and applicability in addressing the mixed uncertainty and CCF of PMS.