The coordinated operation of integrated electricity and heat system is an effective measure to promote renewable energy integration and reduce carbon emissions. Compared to the heat-driven operation mode, the coordinated operation mode of heat and power systems has gained widespread attention due to its higher flexibility. The traditional coordinated heat and power operation based on centralized dispatch assumes that the electricity and heating systems can share information, but in practice, there are information barriers between the two energy sectors. Furthermore, the coordinated operation of heat and power systems typically centers around the power system, resulting in the heating system bearing more costs, which makes it difficult to effectively incentivize the heating system to participate in coordinated operation. In this regard, from the perspective of maximizing overall system benefits, this study first addresses optimization problem of the coordinated operation through distributed solution to protect the privacy of each entity involved. Then, based on the Nash-Harsanyi bargaining game theory, an incentive mechanism that considers risk preferences is proposed to redistribute benefits for maximizing overall system gains, thereby motivating the heating system to participate in coordinated operation. Finally, the effectiveness of the proposed approach is validated in an IEEE-6 node integrated electricity and heat system through simulations. The results demonstrate that compared to the heat-driven operation mode, the distributed-coordinated operation of heat and power systems with the incentive mechanism reduces the operating cost of the electricity system by 7.5% and increases the profit of the heating system by 57.2%.