Given that the neural and connective tissues of the optic nerve head (ONH) exhibit complex morphological changes with the development and progression of glaucoma, their simultaneous isolation from optical coherence tomography (OCT) images may be of great interest for the clinical diagnosis and management of this pathology. A deep learning algorithm was designed and trained to digitally stain (i.e. highlight) 6 ONH tissue layers by capturing both the local (tissue texture) and contextual information (spatial arrangement of tissues). The overall dice coefficient (mean of all tissues) was $0.91 \pm 0.05$ when assessed against manual segmentations performed by an expert observer. We offer here a robust segmentation framework that could be extended for the automated parametric study of the ONH tissues.