There is growing evidence that suggests the importance of astrocytes as elements for neural information processing through the modulation of synaptic transmission. A key aspect of this problem is understanding the impact of astrocytes in the information carried by compound events in neurons across time. In this paper, we investigate how the astrocytes participate in the information integrated by individual neurons in an ensemble through the measurement of "integrated information." We propose a computational model that considers bidirectional communication between astrocytes and neurons through glutamate-induced calcium signaling. Our model highlights the role of astrocytes in information processing through dynamical coordination. Our findings suggest that the astrocytic feedback promotes synergetic influences in the neural communication, which is maximized when there is a balance between excess correlation and spontaneous spiking activity. The results were further linked with additional measures such as net synergy and mutual information. This result reinforces the idea that astrocytes have integrative properties in communication among neurons.