Quantitative assessment of the complex morphological and structural changes of cells and organelles during senescence is critical for understanding the level of senescence, which is a key step toward developing anti-aging therapeutics and preventing aging-related diseases. Despite its importance, a robust quantitative method for evaluating cellular senescence is still lacking. Recent advances in holotomography (HT), a label-free imaging technique, address these challenges by enabling high-contrast cell imaging with subcellular specificity, which enables accurate detection and characterization of senescent cells, without the constraints of fluorescence-based imaging. In this study, we introduce an artificial intelligence (AI)-powered Biologically Interpretable Contrastive and Attention-based Network integrated with HT, called BICAN-HT, which leverages high-resolution images to analyze nucleus-cytoplasm interactions for biologically interpretable and quantitative assessment of cellular senescence with enhanced predictive power. We conducted in-depth experiments inducing cellular senescence using three stressors, including hydrogen peroxide (H2O2), doxorubicin (Dox), and palbociclib (Pal), across two different cell lines. BICAN-HT consistently outperformed current state-of-the-art models across multiple stress conditions and cell types, while capturing the morphological features and spatial relationships of cells and organelles within the nucleus and cytoplasm during senescence. BICAN-HT has the potential to transform aging research and accelerate the development of anti-aging interventions.