The objective of the study described in this paper was to develop an efficient uncertainty quantification framework capable of analyzing uncertainty in integrated spacecraft system models. Specifically, this paper discusses the capabilities of the developed framework and the results when applied to the multidisciplinary analysis of a reusable launch vehicle (RLV). This particular framework is capable of efficiently propagating mixed (inherent and epistemic) uncertainties through complex simulation codes. The Second-Order Probability Theory utilizing a stochastic response surface obtained with Point-Collocation Non-Intrusive Polynomial Chaos was used for the propagation of the mixed uncertainties. This particular methodology was applied to the RLV analysis, and the uncertainty in the output parameters of interested was obtained in terms of intervals at various probability levels. This study has also demonstrated the feasibility of the developed uncertainty quantification framework for efficient propagation of mixed uncertainties in the analysis of complex aerospace systems.