Intermediate-temperature (IT) proton-exchange membranes (PEMs) play vital roles in hydrogen and direct liquid fuel cells, electrolyzers, and other electrochemical membrane reactors at elevated temperatures of higher than 150 °C. This article reports the fabrication and performance assessment of a type of new IT polymer–inorganic composite (PIC) PEMs that were made of cerium ultraphosphate (CeP5O14-CUP) as the durable solid-state proton conductor and undoped polybenzimidazole (PBI) as the high-temperature (HT) polymeric binder. The proton conductivity and electrochemical performance of the PIC PEMs were characterized at 200 °C with varying membrane thickness, processing parameters, and operating conditions using a single-stack hydrogen fuel cell connected to a fuel cell test station. Experimental results show that the PIC membranes (with CUP of 75 wt.%) carried high mechanical flexibility and strength as well as noticeably reduced water uptake of 4.4 wt.% compared to pristine PBI membranes of 14.0 wt.%. Single-stack hydrogen fuel cell tests at 200 °C in a humidified hydrogen and air environment showed that the proton conductivity of the PIC PEMs was measured up to 0.105 S/cm, and the electrochemical performance exhibited its dependence upon the membrane thickness with the power density of up to 191.7 mW/cm2. Discussions are made to explore performance dependence and improvement strategies. The present study expects the promising future of the IT-PIC-PEMs for broad applications in high-efficiency electrochemical energy conversion and value-added chemical production at elevated temperatures of 200 °C or higher.