Implementing integrated electric-heat systems (IEHSs) with coupled power distribution networks and district heating networks is an essential means to solve current energy problems. However, prosumers with multiple energy forms coupled and renewable energy sources with natural uncertainties pose challenges to the operation of IEHSs. This paper proposes a joint energy and reserve dispatch model for IEHSs based on transactive energy, which is a coordinated combination of a bi-level Stackelberg game and two-stage robust optimization. The bi-level Stackelberg game is used to realize the equilibrium of interests among three transacting parties, namely, integrated energy service provider (IESP), multi-carrier prosumer (MCP), and load aggregator (LA). The two-stage robust optimization is employed to ensure the reliability of the system operation under renewable energy uncertainty. In the upper level of the Stackelberg game, the IESP perform pricing and reserve dispatch, while the MCP and LA maximize their benefits via energy management in the lower level. Linearization techniques are utilized to approximate the bi-level Stackelberg game model into a single-level mixed-integer linear programming problem. The converted single-level game model is subsequently regarded as the first stage, while the real-time feasibility check is regarded as the second stage to form a two-stage robust optimization model, which is solved by a modified C&CG algorithm. Case studies demonstrate that the proposed joint energy and reserve dispatch method effectively achieves economic and reliable operation.