Solid-state lithium-metal batteries have great potential to simultaneously achieve high safety and high energy density for energy storage. However, the low ionic conductivity of the solid electrolyte and large electrode/electrolyte interfacial impedance are bottlenecks. A composite solid electrolyte (CSE) that integrates electrospun Li0.33La0.557TiO3 (LLTO) nanofibers, poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP), and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) is fabricated in this work. The effects of the LLTO filler fraction and morphology (spherical vs fibrous) on CSE conductivity are examined. Additionally, a fluorine-rich interlayer based on succinonitrile, fluoroethylene carbonate, and LiTFSI, denoted as succinonitrile interlayer (SNI), is developed to reduce the large interfacial impedance. The use of SNI rather than a conventional ester-based interlayer (EBI) effectively decreases the Li//CSE interfacial resistance and suppresses unfavorable interfacial side reactions. The LiF- and CFx-rich solid electrolyte interphase (SEI), derived from SNI, on the Li metal electrode, mitigates the accumulation of dead Li and excessive SEI. Importantly, dehydrofluorination reactions of PVDF-HFP are significantly reduced by the introduction of SNI. A symmetric Li//CSE//Li cell with SNI exhibits a much longer cycle life than that of an EBI counterpart. A Li//CSE@SNI//LiFePO4 cell shows specific capacities of 150 and 112 mAh g-1 at 0.1 and 2 C (based on LiFePO4), respectively. After 100 charge-discharge cycles, 98% of the initial capacity is retained.