Cardiovascular disease (CVD) is the main cause of death worldwide. Cardiac adipose tissue (CAT) around the heart correlates with CVD risk. MRI and CT scans are preferred for CAT quantification. Ultrasound (US) is limited to linear CAT thickness measurements on the right ventricle. Comprehensive CAT volume and distribution quantification with US could aid CVD assessment. This study uses deep learning to automatically segment the left myocardium (LM), left epicardium (LE), and right epicardium (RE) boundaries in echocardiograms. A U-Net ResNet34 model was trained using 506 expert-traced images. Data was split into 70/10/20 training/validation/test sets. The model achieved Dice scores of 0.94, 0.89, and 0.88 for the three boundaries respectively. Regions-of-interest (ROIs) around the combined left and right epicardium contours were classified as containing CAT or not using spectral analysis of raw RF data. MRI expert-traced images of the same patients provided ground truth labels for CAT. A total of 102 corresponding US-MRI image pairs were matched using visual assessment and anatomical landmarks. ROIs were defined around the predicted epicardium contours, and for each ROI, 9 spectral parameters were computed as a random forest classifier input. A randomized 75/25 training/test split was used. The classifier achieved an average accuracy of 76%, sensitivity of 85%, and specificity of 74%. Results show the feasibility of performing automatic CAT assessment involving echocardiogram segmentation, contour detection, and classification of ROIs around the perimeter of the left and right epicardium in short-axis echocardiograms.