Astrocytes, an integral part of the nervous system in the brain, are now known that they have important roles including the regulation of synaptic transmission and formation, as well as plasticity. Thus, in the current study, we have numerically investigated the effects of astrocyte on the weak signal detection and transmission performances of neurons in tripartite synapse model located in a chaotic environment. Our analyses have shown that the weak signal detection performance of the presynaptic neuron exhibits a chaotic resonance phenomenon that depends on both the intensity of chaotic signal and the frequency of weak signal in the absence of astrocyte. When the astrocytic effects come into play a double chaotic resonance effect emerges depending on the frequency of weak signal, and the strength of resonance obtained is doubled. In the absence of astrocyte, weak signal transmission from the presynaptic neuron to the postsynaptic one is not achieved for any of weak signal frequencies investigated. However, when the astrocyte tuned the excitability of the pre and postsynaptic neurons, that is, when it acted on both, a specific weak signal detected with the best performance by the presynaptic neuron has been transmitted to postsynaptic neuron efficiently. Obtained results uncovered that this efficient transmission has been required some optimal values of astrocyte parameters as well as an optimal coupling strength between pre and postsynaptic neurons. These results suggest a new perspective on the functioning of the nervous system, specifically transmission of weak signals through chaotic resonance, and show that astrocytes play a key role in neuronal information processing and information transfer between neurons.