The rapid development of an integrated energy system makes it difficult for traditional power market to adapt to the trend of multi-energy interactions. Therefore, a tri-layer multi-energy day-ahead market structure and operation mechanism, allowing the simultaneous trading of electricity, heat and natural gas, are proposed in this paper. Concentrating on the profit of the load serving entity in this market, the optimal transaction strategy based on the integrated demand response is explicitly modeled in detail. In particular, the physical constraints of the power distribution network, natural gas network and district heating network are strictly considered. To address the nonlinear and nonconvex problems in the distribution network and natural gas network, the mixed integer second-order cone programming method and piecewise linearization process are used. Furthermore, a novel conditional value at risk approach is proposed to address the uncertain forecasted market prices, so that the risk can be mitigated. Compared with the traditional electricity market, the LSE can earn a higher profit in the proposed market, and the integrated demand response program enhances the potential of multi-energy peak load shifting. Finally, the effectiveness of the proposed method has been verified on an integrated energy system with IEEE 33-bus power system, an 11-node gas system and a 6-node heat system. A set of comparative cases verify the necessity for the IES to keep the balance between the market economy and network security operation.