Due to the capacity of thermal storage, electric water heater (EWH) is one of the best candidates for demand response programs. However, few attentions are given to the modeling and optimization of EWHs with thermostatically-controlled automatic water mixer (TCAWM). In this paper, differential thermodynamic model is established for EWHs with TCAWM and a piecewise linear approximation method is performed for the nonlinear thermodynamic model. The multi-objective optimization model is established by introducing an index reflecting the comfort degree of users, so that the optimal energy usage of the EWH can be obtained by mixed integer linear programming. Testing examples verify the effectiveness of the proposed method.