Due to the growing penetration of renewable energies (REs) in integrated energy system (IES), it is imperative to assess and reduce the negative impacts caused by the uncertain REs. In this paper, an unscented transformation-based mean-standard (UT-MS) deviation model is proposed for the stochastic optimization of cost-risk for IES operation considering wind and solar power correlated. The unscented transformation (UT) sampling method is adopted to characterize the uncertainties of wind and solar power considering the correlated relationship between them. Based on the UT, a mean-standard (MS) deviation model is formulated to depict the trade-off between the cost and risk of stochastic optimization for the IES optimal operation problem. Then the UT-MS model is tackled by a multi-objective group search optimizer with adaptive covariance and Le′vy flights embedded with a multiple constraints handling technique (MGSO-ACL-CHT) to ensure the feasibility of Peratooptimal solutions. Furthermore, a decision making method, improve entropy weight (IEW), is developed to select a final operation point from the set of Perato-optimal solutions. In order to verify the feasibility and efficiency of the proposed UT-MS model in dealing with the uncertainties of correlative wind and solar power, simulation studies are conducted on a test IES. Simulation results show that the UT-MS model is capable of handling the uncertainties of correlative wind and solar power within much less samples and less computational burden. Moreover, the MGSOACL- CHT and IEW are also demonstrated to be effective in solving the multi-objective UT-MS model of the IES optimal operation problem.