In vitro models of normal mammary epithelium have correlated increased extracellular matrix (ECM) stiffness with malignant phenotypes. However, the role of increased stiffness in this transformation remains unclear because of difficulties in controlling ECM stiffness, composition and architecture independently. Here we demonstrate that interpenetrating networks of reconstituted basement membrane matrix and alginate can be used to modulate ECM stiffness independently of composition and architecture. We find that, in normal mammary epithelial cells, increasing ECM stiffness alone induces malignant phenotypes but that the effect is completely abrogated when accompanied by an increase in basement-membrane ligands. We also find that the combination of stiffness and composition is sensed through β4 integrin, Rac1, and the PI3K pathway, and suggest a mechanism in which an increase in ECM stiffness, without an increase in basement membrane ligands, prevents normal α6β4 integrin clustering into hemidesmosomes.