This paper proposes a distributed robust optimal dispatch model to enhance information security and interaction among the operators in the regional integrated energy system (RIES). Our model regards the distribution network and each energy hub (EH) as independent operators and employs robust optimization to improve operational security caused by wind and photovoltaic (PV) power output uncertainties, with only deterministic information exchanged across boundaries. This paper also adopts the alternating direction method of multipliers (ADMM) algorithm to facilitate secure information interaction among multiple RIES operators, maximizing the benefit for each subject. Furthermore, the traditional ADMM algorithm with fixed step size is modified to be adaptive, addressing issues of redundant interactions caused by suboptimal initial step size settings. A case study validates the effectiveness of the proposed model, demonstrating the superiority of the ADMM algorithm with adaptive step size and the economic benefits of the distributed robust optimal dispatch model over the distributed stochastic optimal dispatch model.