The integrated energy system is a perfect way to realize the transformation of the traditional energy industry structure. To further explore the role of its load-side adjustable potential in carbon emission reduction, an optimal operation model of the integrated energy system considering the carbon emission sensing measurement system and demand response (DR) is proposed. First, the integrated electricity–heat energy system (IEHS) model framework is constructed in accordance with the coupling characteristics of electricity–heat–gas in the system. The carbon emission sensing measurement system is introduced on the energy supply side, and DR is considered on the user load side, including the DR model based on the price elasticity matrix and the replacement-based DR model considering the mutual conversion of electric and thermal energies on the energy use side. Second, the baseline method is used to allocate carbon emission quotas for the system free of charge, and the actual carbon emissions of gas turbines and gas boilers are considered. An IEHS objective function is established to minimize the sum of the energy purchase, carbon transaction, and operation and maintenance costs. Third, an improved northern goshawk optimization (INGO) algorithm is proposed to optimize the low-carbon operation of the IEHS model. Finally, the effectiveness and practicability of the proposed model and algorithm are verified using different scenarios and different algorithms. The results show that, considering the carbon emission sensing measurement system and DR, the total operation cost is reduced by 10.4% and the actual carbon emission is reduced by 6420.582 kg. Compared with those of the northern goshawk (NGO) algorithm, the total operation cost of the INGO algorithm is reduced by 9.4% and the actual carbon emission is reduced by 1164.253 kg, which realizes the coordinated operation of system economy and low carbon emission.