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Integrating heating and electricity networks offers extra flexibility to the energy system operation while improving energy utilization efficiency. This paper proposes a data-driven joint distributionally robust chance-constrained (DRCC) operation model for multiple integrated electricity and heating systems (IEHSs). Flexible reserve resources in IEHS are exploited to mitigate the uncertainty of renewable energy. A distributed and parallel joint DRCC operation framework is developed to preserve the decision-making independence of multiple IEHSs, where the optimized CVaR approximation (OCA) approach is developed to transform the local joint DRCC model into a tractable model. An alternating minimization algorithm is presented to improve the tightness of OCA for joint chance constraints by iteratively tuning the OCA. Case studies on the IEEE 33-bus system with four IEHSs and the IEEE 141-bus system with eight IEHSs demonstrate the effectiveness of the proposed approach.