The high prevalence of sleep apnea and the limitations of polysomnography have prompted the investigation of strategies aimed at automated diagnosis using a restricted number of physiological measures. This study aimed to demonstrate that thoracic (THO) and abdominal (ABD) movement signals are useful for accurately estimating the severity of sleep apnea, even if central respiratory events are present. Thus, we developed 2D-convolutional neural networks (CNNs) jointly using THO and ABD to automatically estimate sleep apnea severity and evaluate the central event contribution. Our proposal achieved an intraclass correlation coefficient (ICC) = 0.75 and a root mean square error (RMSE) = 10.33 events/h when estimating the apnea-hypopnea index, and ICC = 0.83 and RMSE = 0.95 events/h when estimating the central apnea index. The CNN obtained accuracies of 94.98%, 79.82%, and 81.60% for 5, 15, and 30 events/h when evaluating the complete apnea hypopnea index. The model improved when the nature of the events was central: 98.72% and 99.74% accuracy for 5 and 15 events/h. Hence, the information extracted from these signals using CNNs could be a powerful tool to diagnose sleep apnea, especially in subjects with a high density of central apnea events.