The demand response, as an effective means of carbon reduction in the demand side, generally uses carbon emission factor (CEF) to evaluate the carbon emissions. However, in the existing research, the output of demand-side renewable energy units is neglected in CEF, which will lead to an inaccurate assessment of carbon emissions and is not helpful for the carbon reduction by the demand response. In this paper, a bi-level incentive-based integrated demand response (IBIDR) approach is proposed to reduce the carbon emission cost with multi-energy time-varying CEFs. In particular, the multi-energy time-varying CEFs model is proposed considering the demand-side proportion of solar output in the total energy consumption. To explore the role of CEF in IBIDR, the coupling effect of the multi-energy time-varying CEFs on the response willingness model is constructed to promote the interaction among different energy resources to reduce the carbon emission. Finally, the proposed bi-level IBIDR optimization model is transformed into a single-level nonlinear problem based on the backward induction method, which can obtain the optimal incentive strategy of IBIDR. Simulation results show the effectiveness of the proposed approach in reducing the incentive cost and carbon emission cost of multi-energy aggregators.