The phospholipid bilayer membrane that surrounds each cell in the body represents the first and last line of defense for preserving overall cell viability. In several forms of cardiac and skeletal muscle disease, deficits in the integrity of the muscle membrane play a central role in disease pathogenesis. In Duchenne muscular dystrophy, an inherited and uniformly fatal disease of progressive muscle deterioration, muscle membrane instability is the primary cause of disease, including significant heart disease, for which there is no cure or highly effective treatment. Further, in multiple clinical forms of myocardial ischemia-reperfusion injury, the cardiac sarcolemma is damaged and this plays a key role in disease etiology. In this review, cardiac muscle membrane stability is addressed, with a focus on synthetic block copolymers as a unique chemical-based approach to stabilize damaged muscle membranes. Recent advances using clinically relevant small and large animal models of heart disease are discussed. In addition, mechanistic insights into the copolymer-muscle membrane interface, featuring atomistic, molecular, and physiological structure-function approaches are highlighted. Collectively, muscle membrane instability contributes significantly to morbidity and mortality in prominent acquired and inherited heart diseases. In this context, chemical-based muscle membrane stabilizers provide a novel therapeutic approach for a myriad of heart diseases wherein the integrity of the cardiac muscle membrane is at risk.