Exergy analysis is a unified approach to evaluating the quantity and quality of energy in integrated energy systems (IESs). However, exergy analysis models have been relatively underexplored for IES operation in energy transmission networks. This study addresses this gap by developing an input-benefit exergy model and an exergy loss calculation model for each link within heat-and-electricity-based IESs (HE-IESs), encompassing the transmission networks. Then, an exergy-based unified optimal operation model for HE-IESs is introduced by minimizing the total exergy loss of the system. In addition, the effect of load rate on the energy efficiency of energy conversion equipment is considered. By applying piecewise linearization to the non-convex terms in the objective function and the equality constraints, the proposed optimization model is accurately and efficiently analyzed as a mixed-integer second-order cone programming problem. The case study results demonstrate that the proposed model reduces equipment-related exergy loss, with approximately 3.2 times the heat network-related exergy loss. Moreover, the average deviation gaps of the overall system's exergy loss and equipment's output exergy power between the proposed and the existing models reach 12.94% and 27.83%, respectively. The maximum relative error of the solution results with the proposed linearization method remains below 1.2%, satisfying the requirements of practical application.