This study monitors neonatal sleep patterns using artificial intelligence through an innovative transfer learning approach integrating video and Electroencephalogram (EEG) data. Leveraging non-intrusive, camera-based technology, this method offers healthcare professionals an effective tool to evaluate and understand sleep quality in newborns. Such monitoring is essential for pediatricians, providing critical insights into the health and development of infants. Automated sleep/wake staging tools aid healthcare professionals in analyzing infant sleep patterns. Among these methods, camera-based approaches have gained prominence due to their non-intrusive and user-friendly characteristics, making them applicable for home monitoring. This study introduces a novel transfer learning technique for classifying neonatal sleep/wake stages. Our approach utilizes multiple color palettes, such as thermal, amber, grayscale, high contrast, hot metal, and red-blue, captured through a Fluke (R) (TiX 580) camera system. Continuous monitoring of neonatal sleep is essential for pediatricians to assess neonatal sleep quality comprehensively. Automated sleep/wake staging tools assist healthcare professionals in evaluating infant sleep patterns. Camera-based approaches have garnered significant attention among the various methods due to their non-intrusive and user-friendly nature, making them suitable for home use. In this paper, we propose a novel transfer learning approach for classifying neonatal sleep/wake staging using a combination of multiple color palettes, including thermal, amber, grayscale, high contrast, hot metal, and red-blue, recorded through a Fluke (R) (TiX 580) camera. The proposed method leverages the retraining of the last fully connected layer of well-established deep neural networks such as Visual Geometry Group 16 and 19, AlexNet, Inception-V3, ResNet-18, ResNet-50, and GoogLeNet to perform accurate sleep and wake stage classification. To enhance the precision of our approach, we integrate EEG data with video data obtained from neonatal subjects. The performance of transfer learning networks is validated using a leave-one-subject-out cross-validation strategy, ensuring robustness in classifying wake and sleep stages. In particular, the Inception-V3 model, when applied to the red-blue color palette video frames, demonstrates an impressive classification accuracy rate of 85.9%. Furthermore, we assessed the impact of including EEG data alongside video data, and even in this context, our approach maintains the same high accuracy of 85.9%. These findings underscore the robustness and effectiveness of our proposed method for neonatal sleep/wake staging classification, which is suitable for home-based monitoring and enhances its practicality and accessibility for pediatricians and caregivers.