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• An exergy analysis model for integrated heat and electricity energy systems. • A joint solution framework for optimization and evaluation based on exergy. • Sequential solution for reducing the complexity of the joint solution problem. • Stringent cutting planes and piecewise linearization for solving and processing. • Exergy-efficient operating mode and key operational information based on exergy. Exergy analysis provides a unified scale for evaluating the quality and quantity of energy, and is suitable and essential for scientifically and rationally guiding the optimization and evaluation of integrated energy systems with intricate multi-component configurations. The present work proposes an exergy analysis model and joint solution framework for integrated energy systems based on exergy, and presents an efficient and accurate solution method. The exergy analysis model is analogous to the energy-based model and possesses a succinct form. This model is then applied to establish an input exergy model defining the exergy of inputs, a destroyed exergy model defining the exergy lost due to the conversions, transmissions, and storages, and a benefit exergy model defining the remaining useful exergy for the loads. The joint solution framework optimizes the system from the basis of exergy conservation, and evaluates the destroyed exergy of each link and the prices of the various exergy products from an economic perspective based on the established exergy analysis model. The complexity of the framework is then reduced by establishing a sequential optimization and evaluation model. The optimization model is solved accurately and efficiently using a stringent cutting plane method to address the problem of relaxation inaccuracy, and piecewise linearization to accommodate the non-convex constraints. Numerical computations on a 97-node system demonstrate the accuracy of the proposed models in exergy-based optimization, destruction, and price evaluation, preventing substantial deviations (e.g., a 23% discrepancy in total destroyed exergy). The adopted cost allocation method based on energy quality reflects fair pricing, rectifying conventional pricing disparities (e.g., a 47.56% underestimation of the electric load using energy-based pricing). Therefore, the accuracy and efficiency of the developed exergy analysis model, solution framework, and solution method are validated. [ABSTRACT FROM AUTHOR]