Purpose: To develop a deep learning approach to digitally-stain optical coherence tomography (OCT) images of the optic nerve head (ONH). Methods: A horizontal B-scan was acquired through the center of the ONH using OCT (Spectralis) for 1 eye of each of 100 subjects (40 normal & 60 glaucoma). All images were enhanced using adaptive compensation. A custom deep learning network was then designed and trained with the compensated images to digitally stain (i.e. highlight) 6 tissue layers of the ONH. The accuracy of our algorithm was assessed (against manual segmentations) using the Dice coefficient, sensitivity, and specificity. We further studied how compensation and the number of training images affected the performance of our algorithm. Results: For images it had not yet assessed, our algorithm was able to digitally stain the retinal nerve fiber layer + prelamina, the retinal pigment epithelium, all other retinal layers, the choroid, and the peripapillary sclera and lamina cribrosa. For all tissues, the mean dice coefficient was $0.84 \pm 0.03$, the mean sensitivity $0.92 \pm 0.03$, and the mean specificity $0.99 \pm 0.00$. Our algorithm performed significantly better when compensated images were used for training. Increasing the number of images (from 10 to 40) to train our algorithm did not significantly improve performance, except for the RPE. Conclusion. Our deep learning algorithm can simultaneously stain neural and connective tissues in ONH images. Our approach offers a framework to automatically measure multiple key structural parameters of the ONH that may be critical to improve glaucoma management.