Sleep staging is a crucial tool for diagnosing and monitoring sleep disorders, but the standard clinical approach using polysomnography (PSG) in a sleep lab is time-consuming, expensive, uncomfortable, and limited to a single night. Advancements in sensor technology have enabled home sleep monitoring, but existing devices still lack sufficient accuracy to inform clinical decisions. To address this challenge, we propose a deep learning architecture that combines a convolutional neural network and bidirectional long short-term memory to accurately classify sleep stages. By supplementing photoplethysmography (PPG) signals with respiratory sensor inputs, we demonstrated significant improvements in prediction accuracy and Cohen's kappa (k) for 2- (92.7 %; k = 0.768), 3- (80.2 %; k = 0.714), 4- (76.8 %, k = 0.550), and 5-stage (76.7 %, k = 0.616) sleep classification using raw data. This relatively translatable approach, with a less intensive AI model and leveraging only a few, inexpensive sensors, shows promise in accurately staging sleep. This has potential for diagnosing and managing sleep disorders in a more accessible and practical manner, possibly even at home.