Problems such as the difficulty of characterizing the dynamic properties of gas and heat networks in the scheduling process of integrated energy systems, and the difficulty of users to intuitively obtain carbon emission information and participate in carbon reduction hinder the development of integrated energy systems. A low-carbon economic dispatch method for integrated energy based on carbon intensity and generalized electrothermal dual response is proposed in this paper. On the one hand, a waste heat recovery device is introduced at the source side to regulate the electrical and thermal loads, and a generalized electrical and thermal demand response is constructed in collaboration with the integrated electrical and thermal demand response. On the other hand, based on the theory of carbon emission flow, the calculation method of carbon emission flow of gas and heat system with dynamic characteristics is derived, and the carbon potential demand response is constructed based on the carbon potential signal. Finally, a low-carbon economic dispatch model is constructed with the objective of optimizing the total system cost in the upper layer and minimizing the system's total carbon emission cost in the lower layer. After the arithmetic verification, the combination of carbon potential-generalized electric-thermal dual-response scheduling reduces the system operating cost by 2.42% and the carbon emission by 7.32% compared with the traditional operation method. The proposed scheduling method realizes the low-carbon economic operation of the system.