Patient-derived organoids and cellular spheroids recapitulate tissue physiology with remarkable fidelity. We investigated how engagement with a reconstituted basement membrane in three dimensions (3D) supports the polarized, stress resilient tissue phenotype of mammary epithelial spheroids. Cells interacting with reconstituted basement membrane in 3D had reduced levels of total and actin-associated filamin and decreased cortical actin tension that increased plasma membrane protrusions to promote negative plasma membrane curvature and plasma membrane protein associations linked to protein secretion. By contrast, cells engaging a reconstituted basement membrane in 2D had high cortical actin tension that forced filamin unfolding and endoplasmic reticulum (ER) associations. Enhanced filamin-ER interactions increased levels of PKR-like ER kinase effectors and ER-plasma membrane contact sites that compromised calcium homeostasis and diminished cell viability. Consequently, cells with decreased cortical actin tension had reduced ER stress and survived better. Consistently, cortical actin tension in cellular spheroids regulated polarized basement membrane membrane deposition and sensitivity to exogenous stress. The findings implicate cortical actin tension-mediated filamin unfolding in ER function and underscore the importance of tissue mechanics in organoid homeostasis.