As an increasing penetration of renewable energy sources can potentially impact voltage profile and compromise system security, the security continues to be the most critical concern in power system operations. A risk-constrained stochastic scheduling model is proposed to leverage the latent scheduling capacity of a multi-energy system to seek an economic operation solution while maintaining system operation risk level against uncertain renewable generation. Overvoltage risk constraints, as compared to the straightforward voltage boundary limits, are incorporated into the stochastic scheduling model to guarantee the operation security and economics. Linearized AC power flow model is applied to enable overvoltage risk assessment within the coordinated scheduling model. The proposed stochastic scheduling model is tackled via the improved progressive hedging approach with an enhanced relax-round-polish process, which overcomes the convergence issues of the traditional progressive hedging in handling nonconvex stochastic scheduling model with binary variables on both stages. Numerical simulation results of IEEE 30-bus system and IEEE 118-bus system illustrate the efficacy of the proposed model in ensuring voltage security and improving economic operation of systems.