The field of nanoionics is of great importance for the development of superior materials for devices that rely on the transport of charged ions, like fuel cells, batteries, and sensors. Often nanostructuring leads to enhanced ionic mobilities due to the induced space-charge effects. Here these large space-charge effects occurring in composites of the proton-donating solid acid CsHSO4 and the proton-accepting TiO2 or SiO2 are studied. CsHSO4 is chosen for this study because it can operate effectively as a fuel-cell electrolyte at elevated temperature while its low-temperature conductivity is increased upon nanostructuring. The composites have a negative enthalpy of formation for defects involving the transfer of protons from the acid to the acceptor. Very high defect densities of up to 10% of the available sites are observed by neutron diffraction. The effect on the mobility of the protons is observed directly using quasielastic neutron scattering and nuclear magnetic resonance spectroscopy. Surprisingly large fractions of up to 25% of the hydrogen ions show orders-of-magnitude enhanced mobility in the nanostructured composites of TiO2 or SiO2, both in crystalline CsHSO4 and an amorphous fraction.