To improve the wind energy dispatchability in the presence of non-Gaussian wind power uncertainties, this paper presents a stochastic coordinated control scheme for the doubly-fed-induction-generator-based wind-battery hybrid systems (WBHS). The proposed control scheme has a two-layer structure. Based on the non-Gaussian distributional wind power forecasts, an upper layer stochastic predictive controller coordinates the operation of wind and battery subsystems. The computed power references are passed to the lower layer wind and battery controllers for execution. This way, the combined power output of WBHS is brought to the desired dispatch levels. The salient feature of the proposed scheme is that it optimizes the control actions over the non-Gaussian wind power predictive distributions, thus handling the non-Gaussian uncertainties in wind power. The simulation results on actual wind data demonstrate the effectiveness of the proposed scheme.