  Top-of-atmosphere (TOA) cosmic-ray (CR) fluxes from satellites and
balloon-borne experiments are snapshots of the solar activity imprinted on the
interstellar (IS) fluxes. Given a series of snapshots, the unknown IS flux
shape and the level of modulation (for each snapshot) can be recovered. We wish
(i) to provide the most accurate determination of the IS H and He fluxes from
TOA data alone, (ii) to obtain the associated modulation levels (and
uncertainties) while fully accounting for the correlations with the IS flux
uncertainties, and (iii) to inspect whether the minimal force-field
approximation is sufficient to explain all the data at hand. Using H and He TOA
measurements, including the recent high-precision AMS, BESS-Polar, and PAMELA
data, we performed a non-parametric fit of the IS fluxes $J^{\rm IS}_{\rm
H,~He}$ and modulation level $\phi_i$ for each data-taking period. We relied on
a Markov chain Monte Carlo (MCMC) engine to extract the probability density
function and correlations (hence the credible intervals) of the sought
parameters. Although H and He are the most abundant and best measured CR
species, several datasets had to be excluded from the analysis because of
inconsistencies with other measurements. From the subset of data passing our
consistency cut, we provide ready-to-use best-fit and credible intervals for
the H and He IS fluxes from MeV/n to PeV/n energy (with a relative precision in
the range [2-10\%] at 1$\sigma$). Given the strong correlation between $J^{\rm
IS}$ and $\phi_i$ parameters, the uncertainties on $J^{\rm IS}$ translate into
$\Delta\phi\approx \pm 30$~MV (at 1$\sigma$) for all experiments. We also find
that the presence of $^3$He in He data biases $\phi$ towards higher $\phi$
values by $\sim 30$~MV. The force-field approximation gives an excellent
($\chi^2/$dof$=1.02$) description of the recent high-precision TOA H and He
fluxes.
