Carotid ultrasound is a screening modality used by physicians to direct treatment in the prevention of ischemic stroke in high-risk patients. It is a time intensive process that requires highly trained technicians and physicians. Evaluation of a carotid ultrasound requires segmentation of the vessel wall, lumen, and plaque of the carotid artery. Convolutional neural networks are state of the art in image segmentation yet there are no previous methods to solve this problem on carotid ultrasounds. We introduce two novel convolutional U-net models for both vessel and plaque from ultrasound images of the entire carotid system. We obtained de-identified images under IRB approval from 226 patients. We isolated a total of 500 ultrasound images spanning the internal, external, and common carotid arteries. We manually segmented the vessel lumen and plaque in each image that we then use as ground truth. In 10-fold cross-validation all models attain over 90% accuracy for vessel segmentation. With a basic convolutional U-Net we obtained an accuracy of 66.8% for plaque segmentation. With our dual-decoder model we see an improvement to 68.8% whereas our two-stage model falls behind at 65.1% accuracy. However, if we gave our two-stage model the true correct vessel as input its plaque accuracy rises to 81.7% suggesting that the method has potential and needs more work. We ensemble our U-Net and dual decoder U-Net models to obtain confidence scores for segmentations. By considering high confidence outputs above the 60% and 80% thresholds the accuracy of our dual decoder U-Net rises to 75.2% and 87.3% respectively. Our work here shows the potential of dual and two-stage methods for vessel and plaque segmentation in carotid artery ultrasound images and is an important first step in creating a system that can independently evaluate carotid ultrasounds.