The dispatch of integrated energy systems in coal mines (IES-CM) with mine-associated supplies is vital for efficient energy utilization and carbon emissions reduction. However, IES-CM dispatch is highly challenging due to its feature as multi-objective and strong multi-constraint. Existing constrained multi-objective evolutionary algorithms often fall into locally feasible domains with poorly distributed Pareto front, which greatly deteriorates dispatch performance. To tackle this problem, we transform the traditional dispatch model of IES-CM into two tasks: the main task with all constraints and the helper task with constraint adaptive. Then we propose a constraint adaptive multi-tasking differential evolution algorithm (CA-MTDE) to optimize these two tasks effectively. The helper task with constraint adaptive is developed to obtain infeasible solutions near the feasible domain. The purpose of this infeasible solution is to transfer guiding knowledge to help the main task move away from local search. Additionally, a dynamic dual-learning strategy using DE/current-to-rand/1 and DE/current-to-best/1 is developed to maintain task diversity and convergence. Finally, we comprehensively evaluate the performance of CA-MTDE by applying it to a coal mine in Shanxi Province, considering two IES-CM scenarios. Results demonstrate the feasibility of CA-MTDE and its ability to generate a Pareto front with exceptional convergence, diversity, and distribution.