Complex networks hosting binary-state dynamics can represent many phenomena in real world systems. Therefore, some approaches were proposed to reconstruct the structures of networks with binary-state dynamics. However, they often hold two assumptions: 1) require a priori knowledge about which state is the active state, or one state is imposed as the active state; and 2) only one side of transition probability is utilized for network reconstruction. Many binary-state dynamics, such as cooperative/defective state in evolutionary game, agree/disagree of two competing opinions, it is hard to define which state is the active state, what’s more, both sides of the transition probability depend on the states of neighbors. For this situation, if we only consider one side of transition probability, the reconstruction accuracy is greatly discounted because many data are not effectively used. By abandoning the two assumptions, we here develop a generalized statistical inference approach by exploiting the expectation-maximization algorithm to reconstruct networks. Our approach requires less information regarding the dynamics, indicating more potential applications. More importantly, our approach sufficiently mines the given data, the results on empirical and synthetic networks demonstrate the high-reconstruction accuracy. In addition, the method is parameter free and robust to the stochastic fluctuations.