In the future integrated energy market, the traditional centralized planning method cannot solve the planning problem for multi-stakeholder integrated energy systems (MSIESs). To cope with this problem, this paper proposes a synchronously decentralized adaptive robust programming (SDARP) model for MSIESs based on the analytical target cascading (ATC) algorithm. In this model, different stakeholders are planned in parallel under the source-load uncertainties, aiming at minimizing the annual investment and operation costs and fully taking into account the interactive heating/cooling power transmitted by the district heating/cooling network. In each stakeholder, the column-and-constraint generation algorithm is used to address the robustness problems in the three-layer adaptive robust programming model. In addition, a tractable alternating optimization procedure is used to solve the non-convex SDARP model with finite convergence. Case studies verify the superiority and effectiveness of the SDARP method in dealing with the planning problem of MSIESs.