The cooperative optimization of multi-stakeholders contributes significantly to the optimal planning of different integrated electricity-heat-gas-hydrogen (IEHGH) investors. The peer-to-peer (P2P) transaction promotes multi-agent planning toward a more economical and interdependent solution. This paper proposes a decentralized robust planning model for multiple IEHGHs, considering the uncertainty of renewable energy sources (RES) and bilateral transactions. First, a robust linear counterpart of RES is adopted to model the short-term uncertainty in typical scenarios to ensure robustness and computation efficiency. Then, a decentralized shadow pricing strategy based on a combined alternating optimization procedure (AOP) and alternating direction multiplier method (ADMM) is developed to handle the non-convexity and protect privacy. The minimization of social cost and convergence of the proposed strategy are guaranteed through theoretical proof. Finally, comparative case studies on three interconnected IEHGHs demonstrate the effectiveness of the proposed co-planning method.