Strain-rate sensitivity and rate-dependent hardness, over a range of 10⁻² to 10² s⁻¹, of sputter-deposited single-layered Cu, Mo, and 5 nm Cu/5 nm Mo, and 100 nm Cu/100 nm Mo multilayer films with a total film thickness of 5 μm were measured using nanoindentation. The plastic zone underneath the nanoindents was characterized via cross-sectional transmission electron microscopy (XTEM). The multilayer films exhibited enhanced hardness but slightly reduced strain-rate sensitivity with decreasing layer thickness from 100 nm to 5 nm. Only the 5 nm Cu/5 nm Mo multilayer film exhibited shear bands underneath the nanoindents, and the size of the shear bands increased with increasing strain rate. In contrast, the 100 nm Cu/100 nm Mo multilayer film exhibited material pile-up around the indents and significant nanotwinning within Cu grains. The effect of strain rate and layer thickness on the hardness and strain rate sensitivity of the multilayer thin films is interpreted using a modified confined layer slip (CLS) model. The reduced rate sensitivity at 5 nm as compared to 100 nm correlates with abundant growth nanotwins in the Cu grains in 100 nm and formation of shear bands in 5 nm multilayers. In single layer films, a substructure with a high density of dislocations was observed consistent with the plastic strain gradient in the indent plastic zone. No evidence of deformation twins was noted in any of the samples.