We study the chaotic resonance phenomenon whereby the response of a neuron to a weak signal is amplified with the help of chaotic current stemming from background activity in the brain. This resonance behavior exhibits a bell-shaped curve in terms of detection quality due to increasing chaotic current intensity. Recent experimental studies have shown that astrocytes, which are the most abundant types of glial cells, may be responsible for the regulation of electrophysiological events in neuronal medium. Hence, we consider here a realistic neuronal system which is constituted by a bipartite network consisting of an excitable neuron and an astrocyte. Our analysis reveals that signal detection quality can be greatly enhanced with the astrocyte contribution obtained by appropriate neuronal and astrocytic cell dynamics. We find that depolarization-induced astrocytic glutamate release is able to improve chaotic resonance performance considerably in the presence of an adequately strong interaction between the astrocyte and the excitable neuron receiving a weak signal with a relatively higher frequency. We also show that a moderate production rate of gliotransmitters is required for the astrocyte to affect resonance performance of the neuron. Except for those conditions where the facilitating effect of astrocyte is observed, it can also reduce signal detection performance in the neuron. Furthermore, we demonstrated that intrinsic neuronal excitability is regulated by the astrocyte, via a comparison of resonance behaviors under effects of bias and astrocytic current separately. Taken together, our findings provide a novel insight into the functioning of astrocyte-neuron circuits, in particular the encoding weak signals via chaotic resonance, and suggest that astrocytes play a key role in intrinsic regulation and selectivity in neuronal information processing.