A state estimation problem is studied for a class of coupled outputs discrete-time networks with stochastic measurements, i.e., the measurements are missing and disturbed with stochastic noise. The considered networks are coupled with outputs rather than states, are coupled with different inner coupling matrices rather than identical inner ones. By using Lyapunov stability theory combined with stochastic analysis, a novel state estimation scheme is proposed to estimate the states of discrete-time complex networks through the available output measurements, where the measurements are stochastic missing and are disturbed with Brownian motions which are caused by data transmission among nodes due to communication unreliability. State estimation conditions are derived in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the validity of the proposed scheme.