Graphite/LiNi0.4Mn1.6O4 cells assembled with a new reinforced polyvinylidene fluoride (pVDF)–nano crystalline cellulose (NCC) separator and EC–DMC 1 M LiFAP electrolyte with additives were tested by deep charge/discharge cycles at different C-rates and by the FreedomCAR DOE protocol to simulate the dynamic functioning of the batteries in power-assist full hybrid electric vehicles (HEVs). The results of this study evidence the beneficial impact of the pVDF–NCC macroporous membrane with respect to the polypropylene monolayer Celgard®2400 separator on the high C-rate cell performance. The deep charge/discharge of the cell with pVDF–NCC at C/1 effective rate provided 101 W h kg−1 to be compared with 85 W h kg−1 of the cell with Celgard®2400 (the cell weight was considered twice the composite electrode weight of both electrodes). Also hybrid pulse power characterization tests based on the FreedomCAR protocol at 5 C and 10 C demonstrated the superior performance of the cells with pVDF–NCC with respect to that of the cells with Celgard®2400 even if both cells exceed the FreedomCAR goals of power and energy for minimum and maximum power-assist HEV.