In order to facilitate energy sharing and improve system flexibility, a hybrid energy sharing framework of multiple microgrids (MGs) is proposed for a heat-electricity integrated energy system with combined heat and power (CHP) and demand response. First, considering the multi-timescale characteristics, an electrical and thermal energy sharing model of interconnected MGs with CHP and photovoltaic systems is built, in which CHP can operate in a hybrid mode by selecting the operating point flexibly. Moreover, the local subproblem of each MG is formulated and solved considering a comprehensive set of factors, including the generating heat and power cast, trading cost with utility grid, trading electrical and thermal energy cost with other MGs, load characteristic, power consumption utility, and thermal discomfort cost. In addition, a distributed optimization algorithm is used to solve the hybrid energy sharing problem, where the electrical and thermal energy prices can be obtained. Finally, the effectiveness of the proposed energy sharing method is demonstrated by a case study simulation.