The increasing penetration of renewable energy resources, higher demand variability, and the growing role of active consumers have introduced new challenges to traditional day-ahead power system operation. Demand response (DR) programs and real-time pricing (RTP) mechanisms offer effective means for improving operational flexibility; however, their coordinated integration into uncertainty-aware day-ahead scheduling models has not been fully investigated. This paper proposes an optimization-based framework that jointly incorporates DR and RTP into a stochastic security-constrained unit commitment (SCUC) model. Load demand and price-related uncertainties are represented through a scenario-based stochastic formulation, enabling simultaneous coordination between generation scheduling decisions and price-responsive demand adjustments. The proposed framework aims to minimize the expected total operating cost while satisfying generation limits, power balance, reserve requirements, ramping constraints, and DR-related operational limitations. The model is evaluated under multiple operating scenarios to examine the effects of coordinated DR and RTP participation on system performance. The simulation results indicate that the proposed framework can reduce total operating cost, enhance demand-side flexibility, and improve the robustness of day-ahead scheduling compared with conventional approaches. These findings suggest that coordinated demand-side participation supported by dynamic pricing mechanisms can contribute to more efficient and reliable day-ahead power system operation under uncertainty.