Given the goal of "double carbon", an integrated energy system dominated by zero-carbon energy such as hydrogen is developing at a high speed. Giving full play to the collaborative optimization of its operation strategy and capacity allocation is conducive to ensuring energy supply and improving planning economy. Given this, an optimal capacity allocation method of an electricity-heat-hydrogen cogeneration system (EHH-CS) with coordinated operation and planning is proposed. First, based on the construction of an EHH-CS model, and through the combination of Latin hypercube sampling and improved K-means clustering, typical scenarios of uncertainties are established to realize the reasonable description of renewable energy and load uncertainty. Second, a double-layer joint iterative model of capacity allocation of an EHH-CS is established. The upper layer is the optimal allocation layer, and this takes the maximum daily net investment income as the objective of optimal allocation, and the lower layer is the optimal operation layer, which takes the maximum daily operation income as the objective of optimal operation. A cyclic iterative solution is carried out using the particle swarm optimization algorithm to obtain the coordinated optimal operation strategy and capacity allocation scheme. Finally, an EHH-CS is taken as an example to verify the simulation. The results show that the proposed method promotes the local consumption of renewable energy and effectively balances the planning and operational costs of the system. This work is supported by the National Key Research and Development Program of China (No. 2020YFB1506802).