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Understanding the underlying mechanism of the propagation of neuronal activities within the brain is a fundamental issue in neuroscience. Traditionally, communication and information processing have been exclusively considered as the province of synaptic coupling between neurons. Astrocytes, however, have recently been acknowledged as active partners in neuronal information processing. So, it is more reasonable and accurate to study the nature of neuronal signal propagation with the participation of astrocytes. In this paper, we first propose a feedforward neuronal-astrocytic network (FNAsN), which includes the mutual neuron-astrocyte interaction. Besides, we also consider the unreliability of both the synaptic transmission between neurons and the coupling between neurons and astrocytes. Then, the performance of firing rate propagation through the proposed FNAsN is studied through a series of simulations. Results show that the astrocytes can mediate neuronal activities, and consequently improve the performance of firing rate propagation, especially in a weak and noisy environment. From this point of view, astrocytes can be regarded as a realistic internal source of noise, which collaborates with an externally applied weak noise to prevent synchronous neuron firing within the same layer and thus to ensure reliable transmission.