The ongoing development of technology has changed the nature of electric networks in the field of electric power generation. In the same vein, the generation units and demands are getting close by the integration of distributed resources within the distribution system with the aim of bringing more advantages to the system. Considering the promising concept of hybrid networks, which comprises different distributed resources, as a supportive element for the power system, this paper mainly focuses on modeling a distributed hybrid network, through which both the AC and DC loads can be supplied within the hybrid network. This network is operated in a distributed way where no independent operator is assumed for the operation. The primal-dual method of multipliers (PDMM) as an effective distributed method handles the operation of this network. So far, this method has only been applied to the AC grid or DC grid separately, while the presented method is modified for the operation of the hybrid network. Convergence speed and preciseness are mentioned as the advantages of this method which dominates the alternating direction method of multipliers (ADMM). In real cases, there are some errors in the output power of the renewable resources. Aiming to make the presented PDMM method more applicable, the uncertainty is also modelled using the Unscented Transform (UT) approach, as a way of uncertainty modelling which has shown attractive features, especially the capability of correlation modelling; therefore, it is more preferable for uncertainty modeling in many cases compared to the other methods. The proposed work is implemented on a smart island and the authenticity of this work is proved by comparing the performance of the proposed distributed approach with the centralized method.