For asymptomatic patients suffering from carotid stenosis, the assessment of plaque morphology is an important clinical task which allows monitoring of the risk of plaque rupture and future incidents of stroke. Ultrasound Imaging provides a safe and non-invasive modality for this, and the segmentation of media-adventitia boundaries and lumen-intima boundaries of the Carotid artery form an essential part in this monitoring process. In this paper, we propose a novel Deep Convolutional Neural Network as a fully automated segmentation tool, and its application in delineating both the media-adventitia boundary and the lumen-intima boundary. We develop a new geometrically constrained objective function as part of the Network's Stochastic Gradient Descent optimisation, thus tuning it to the problem at hand. Furthermore, we also apply a novel, bimodal fusion of envelope and phase congruency data as an input to the network, as the latter provides an intensity-invariant data source to the network. We finally report the segmentation performance of the network on transverse sections of the carotid. Tests are carried out on an augmented dataset of 81,000 images, and the results are compared to other studies by reporting the DICE coefficient of similarity, modified Hausdorff Distance, sensitivity and specificity. Our proposed method is shown to yield results of comparable accuracy over this larger dataset, with the advantage of it being fully automated. We conclude that Deep Convolutional Neural Networks provide a reliable trained manner in which carotid ultrasound images may be automatically segmented, using envelope data and intensity invariant phase congruency maps as a data source.