The energy transition can facilitate the rapid development of the coupled electricity and heat system (CEHS), accommodating the higher share of renewable energy. However, uncertain renewable energy sources (RESs) and overlimit risk can bring significant challenges for the safe operation of the CEHS. Considering uncertain RESs integration and overlimit risk within the upper and lower bounds jointly with high probability, the multistage model predictive control (MPC) co-risk dispatch model for the CEHS can be proposed in this paper. The model can hedge against the operational risk for the multistage rolling dispatch. In the context of the multistage real-time risk dispatch, the MPC framework is presented, which contains three processes, autoregressive moving average (ARMA) model prediction process, risk-based optimization process, and penalty-based feedback correction process. In the prediction process, the ARMA method can be employed to accurately predict the RESs power, which is characterized as the merit of the short-term forecast. In the optimization process, the violation risk of overlimit chance constraints caused by the output power fluctuation can be mitigated using the distributionally robust chance-constrained (DRCC) under the Wasserstein ambiguity set. The tractable approximation reformulation can be obtained by adopting the Worst-Case Conditional Value-at-Risk (WC-CVaR) approximation method. In the feedback correction process, penalty-based load shedding and RESs spillage can lower the risk level by minimizing the risk penalty cost. In the numerical case, the risk performance analysis based on the modified Barry Island system is implemented. The analysis demonstrates that the daily average violation probability <inline-formula> <tex-math notation="LaTeX">$V_{p}$ </tex-math></inline-formula> can be mainly affected by the Wasserstein radius <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> while the total cost <inline-formula> <tex-math notation="LaTeX">$C_{obj}$ </tex-math></inline-formula> can be affected by the violation probability <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>. The dispatch energy for the CEHS is obtained using the proposed approach, which outperforms the existing robust optimization (RO) approach.