The accuracy of sleep posture assessment in standard polysomnography might be compromised by the unfamiliar sleep lab environment. In this work, we aim to develop a depth camera-based sleep posture monitoring and classification system for home or community usage and tailor a deep learning model that can account for blanket interference. Our model included a joint coordinate estimation network (JCE) and sleep posture classification network (SPC). SaccpaNet (Separable Atrous Convolution-based Cascade Pyramid Attention Network) was developed using a combination of pyramidal structure of residual separable atrous convolution unit to reduce computational cost and enlarge receptive field. The Saccpa attention unit served as the core of JCE and SPC, while different backbones for SPC were also evaluated. The model was cross-modally pretrained by RGB images from the COCO whole body dataset and then trained/tested using dept image data collected from 150 participants performing seven sleep postures across four blanket conditions. Besides, we applied a data augmentation technique that used intra-class mix-up to synthesize blanket conditions; and an overlaid flip-cut to synthesize partially covered blanket conditions for a robustness that we referred to as the Post-hoc Data Augmentation Robustness Test (PhD-ART). Our model achieved an average precision of estimated joint coordinate (in terms of PCK@0.1) of 0.652 and demonstrated adequate robustness. The overall classification accuracy of sleep postures (F1-score) was 0.885 and 0.940, for 7- and 6-class classification, respectively. Our system was resistant to the interference of blanket, with a spread difference of 2.5%.