Microgrid and distribution network have mutual influences and constraints when interactive operation. Thus, it is necessary to integrate interests of microgrid and distribution network together in order to benefit the entire system. Microgrid and distribution network, as two objectives that need to be optimized at the same time, have some conflicts of interests. The interaction of microgrid and distribution network is studied when interactive operation to analyze their operation benefits respectively. The benefit objectives are modeled as virtual game participants to establish models and fuzzy mathematics method is applied to generalize the benefit functions to membership. In combination with evolutionary game theory and cooperative co-evolutionary algorithm, a co-evolutionary game algorithm is proposed to solve the problem. Then, a maximum dissatisfaction based dynamic optimal sub-model considering the randomness of distributed energy is established to make dynamic adjustments in co-evolutionary game algorithm. A typical Europe microgrid connected with IEEE 33 distribution network is simulated and a simulation with multi-objective optimization method is also carried out for comparison. The results show that the final optimal stable strategy allows the entire microgrid and distribution network to achieve the best operation, thus the effectiveness and superiority of the proposed model and algorithm are proved. This work is supported by National Natural Science Foundation of China (No. 51577115).