Integrated demand response contributes to flexibility improvement in multi-energy system. Yet, the challenge posed by the load estimation mistake needs to be addressed to explore the available flexibility. In this paper, we present a price-based nonlinear integrated demand response for multi-energy microgrid against estimation mistakes of both electricity and gas loads. Among them, we develop a period partition method to describe load characteristics and reach a reasonable time-of-use pricing. Besides, a credibility theory-based risk measurement is presented to evaluate the uncertain wind power. Finally, case studies demonstrate the feasibility and effectiveness of the proposed method in flattening load curve, reducing operation cost and promoting the accommodation of wind power.INDEX TERMS Credibility, flexibility, integrated demand response, load mistake, multi-energy system.