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The increasing utilization of cogeneration plants and energy conversion facilities accelerates the integration of energy systems, which introduces both opportunities and challenges into system operation and management. Thorough mathematical models and analytical methods that take into account the energy flow interdependence and strategic behaviors in multi-carrier energy systems are highly desired. This paper studies an integrated heat-power distribution system from the market perspective. The nonlinear AC optimal power flow (OPF) model is used to clear the distribution power market, which exactly accounts for network losses. To facilitate computation, convex relaxation is applied and polyhedral outer approximation of second-order cone is performed, leading to a linear market clearing model. An optimal thermal flow (OTF) model is employed to clear the heat market. Energy consumptions of heating devices are charged according to locational marginal prices. The market equilibrium is interpreted by a fixed point between OPF and OTF and reformulated as a mixed-integer linear program. Dedicated optimization models are set forth to investigate the market impact of strategic providers and elastic demands in which the market equilibrium condition serves as constraint. Case studies validate the effectiveness of the proposed model and method.