Current techniques for tracking sleep are either obtrusive (Polysomnography) or low in accuracy (wearables). In this early work, we model a sleep classification system using an unobtrusive Ballistocardiographic (BCG)-based heart sensor signal collected from a commercially available pressuresensitive sensor sheet. We present DeepSleep, a hybrid deep neural network architecture comprising of CNN and LSTM layers. We further employed a 2-phase training strategy to build a pre-trained model and to tackle the limited dataset size. Our model results in a classification accuracy of 74%, 82%, 77% and 63% using Dozee BCG, MIT-BIH's ECG, Dozee's ECG and Fitbit's PPG datasets, respectively. Furthermore, our model shows a positive correlation (r = 0.43) with the SATED perceived sleep quality scores. We show that BCG signals are effective for long-term sleep monitoring, but currently not suitable for medical diagnostic purposes. CCS CONCEPTS • Human-centered computing → Ubiquitous computing.