In the coal mining process, a large amount of Coal Mine-Associated energy (CMAE), such as coal mine methane and underground wastewater, is produced. Research on the modeling and optimization dispatching of a Coal Mine-Integrated Energy System (CMIES) with CMAE effectively saves energy and reduces carbon pollution. CMAE has great uncertainties owing to the affections of the hydrogeology conditions and mining schedules. In addition, thermal loads have high comfort requirements in mines, which brings great challenges to the optimization dispatching of CMIESs. Therefore, this paper studies the architecture and solution of CMIESs with a flexible thermal load and source-load uncertainty. First, to effectively improve the electric and thermal conversion efficiency, the architecture of CMIES, including a concentrating solar power station, is built. Second, for the scheduling model with bilateral uncertainty, the interval representation method with interval variables is proposed, and a multi-objective scheduling model based on the interval variables and flexible thermal load is constructed. Finally, we propose a solution method for the model with interval variables. A case study is conducted to demonstrate the performance of our model and method for lowering carbon emissions and cost.