High penetration and fluctuation of renewable energy resources are threatening the voltage security of the integrated hybrid energy system (IHES). This article focuses on providing a fully distributed method to ensure the voltage security and information privacy of the IHES. First, a multiagent system based control scheme is presented, in which the upper level agent is responsible for the voltage security of the whole system, and the local dynamic performance of each distributed energy resource (DER) unit is formulated in the lower level unit agent. Second, a distributed model predictive control (DMPC) based coordinated voltage control method is proposed, by which only partial information exchange is needed in the interaction. Furthermore, the diverse requirements on voltage quality of each microgrid in the IHES are considered in this article and it provides a novel paradigm in this field compared with the traditional methods. To study the stability of the resultant DMPC, the Nash equilibrium is achieved and theoretically proved to ensure the convergence of the proposed method. Finally, the validity of the proposed method is verified by virtue of the simulation and experimental test results.