Cooperation between electric power networks (EPNs) and district heating networks (DHNs) has been extensively studied under the assumption that all information exchanged is authentic. However, EPNs and DHNs belonging to different entities may result in marketing fraud. This paper proposes a cooperation mechanism for integrated electricity-heat systems (IEHSs) to overcome information asymmetry. First, a fraud detection method based on multiparametric programming with guaranteed feasibility reveals the authenticity of the information. Next, all honest entities are selected to form a coalition. Furthermore, to maintain operational independence and distribute benefits fairly, Benders decomposition is enhanced to calculate Shapley values in a distributed fashion. Finally, the cooperative surplus generated by the coalition is allocated according to the marginal contribution of each entity. Numerical results show that the proposed mechanism stimulates cooperation while achieving Pareto optimality under asymmetric information.