Hemianopic patients retain some abilities to integrate audiovisual stimuli in the blind hemifield, showing both modulation of visual perception by auditory stimuli and modulation of auditory perception by visual stimuli. Indeed, conscious detection of a visual target in the blind hemifield can be improved by a spatially coincident auditory stimulus (auditory enhancement of visual detection), while a visual stimulus in the blind hemifield can improve localization of a spatially coincident auditory stimulus (visual enhancement of auditory localization). To gain more insight into the neural mechanisms underlying these two perceptual phenomena, we propose a neural network model including areas of neurons representing the retina, primary visual cortex (V1), extrastriate visual cortex, auditory cortex and the Superior Colliculus (SC). The visual and auditory modalities in the network interact via both direct cortical-cortical connections and subcortical-cortical connections involving the SC; the latter, in particular, integrates visual and auditory information and projects back to the cortices. Hemianopic patients were simulated by unilaterally lesioning V1, and preserving spared islands of V1 tissue within the lesion, to analyze the role of residual V1 neurons in mediating audiovisual integration. The network is able to reproduce the audiovisual phenomena in hemianopic patients, linking perceptions to neural activations, and disentangles the individual contribution of specific neural circuits and areas via sensitivity analyses. The study suggests i) a common key role of SC-cortical connections in mediating the two audiovisual phenomena; ii) a different role of visual cortices in the two phenomena: auditory enhancement of conscious visual detection being conditional on surviving V1 islands, while visual enhancement of auditory localization persisting even after complete V1 damage. The present study may contribute to advance understanding of the audiovisual dialogue between cortical and subcortical structures in healthy and unisensory deficit conditions.