The resonant charge exchange coupling between H+, H, O+ and O is a major driver of H+ and O+ transport between the plasmasphere and topside ionosphere. In this work, we present a new technique to derive model-independent neutral atomic hydrogen density, [H], based on parametric solution of the proton continuity equation including charge-exchange-driven transport. Estimation of [H] using the proton continuity equation incorporates atomic oxygen density [O] derived from the inversion of 135.6 nm OI emission measured by TIMED/GUVI and coincident ionospheric parameter measurements from the Arecibo incoherent scatter radar. Furthermore, by solving both the H+ and O+ continuity equations simultaneously, this work also quantifies the field-aligned vertical transport of protons between the plasmasphere and ionosphere and its effect on maintenance of the nightside and dayside ionospheric composition. Case studies during geomagnetically quiet intervals show that the transport of protons from the plasmasphere during nighttime is sufficient for the maintenance of the observed ionospheric O+ composition through reverse charge-exchange with O. Resulting O+ can diffuse upward or downward away from the source, which leads to observed counter-streaming of H+ and O+. Higher O+ densities on the dayside result in the charge-exchange production of H+, which acts as a source of protons to the plasmasphere. In summary, this work provides an unprecedented, model-independent quantification of diurnal conservation of plasmaspheric protons and its effect on ionospheric variability during quiet-times.