Precise and automated segmentation of the liver and its tumor within CT scans plays a pivotal role in swift diagnosis and the development of optimal treatment plans for individuals with liver diseases and malignancies. However, automated liver and tumor segmentation faces significant hurdles arising from the inherent heterogeneity of tumors and the diverse visual characteristics of livers across a broad spectrum of patients. Aiming to address these challenges, we present a novel Transformer-aware Multiscale Progressive Encoder-Decoder Network (T-MPEDNet) for automated segmentation of tumor and liver. T-MPEDNet leverages a deep adaptive features backbone through a progressive encoder-decoder structure, enhanced by skip connections for recalibrating channel-wise features while preserving spatial integrity. A Transformer-inspired dynamic attention mechanism captures long-range contextual relationships within the spatial domain, further enhanced by multi-scale feature utilization for refined local details, leading to accurate prediction. Morphological boundary refinement is then employed to address indistinct boundaries with neighboring organs, capturing finer details and yielding precise boundary labels. The efficacy of T-MPEDNet is comprehensively assessed on two widely utilized public benchmark datasets, LiTS and 3DIRCADb. Extensive quantitative and qualitative analyses demonstrate the superiority of T-MPEDNet compared to twelve state-of-the-art methods. On LiTS, T-MPEDNet achieves outstanding Dice Similarity Coefficients (DSC) of 97.6% and 89.1% for liver and tumor segmentation, respectively. Similar performance is observed on 3DIRCADb, with DSCs of 98.3% and 83.3% for liver and tumor segmentation, respectively. Our findings prove that T-MPEDNet is an efficacious and reliable framework for automated segmentation of the liver and its tumor in CT scans.