One considerable concern in metallic glass is enhancing ductility by suppressing catastrophic failure by the instantaneous propagation of shear bands. Compressed nanopillars with alternating CuZr metallic glass and polyisoprene nanolaminates exhibit >30% enhancement in plastic flow, as compared with monolithic glass, without sacrifice of strength. A suppression of stochastic strain burst signature in these metallic glass-polymer composites is reported, which is an undesirable characteristic ubiquitously present in monolithic metallic glass and in metallic glass-metal composites. The intermittent stochastic signature is quantified in each metallic glass-containing nanolaminate system by constructing histograms of burst size distributions and provide theoretical foundation for each behavior. The exceptional mechanical properties emergent in these MG-polymer nanolaminate composites are attributed to the combination of nanometer size-induced shear band suppression in metallic glasses and the damping capability of the polyisoprene layers.