  We present the first systematic measurement of the binding energy $E_a$ of
hydrogen atoms to the surface of saturated $^3$He-$^4$He mixture films. $E_a$
is found to decrease almost linearly from 1.14(1) K down to 0.39(1) K, when the
population of the ground surface state of $^3$He grows from zero to
$6\times10^{14}$ cm$^{-2}$, yielding the value $1.2(1)\times 10^{-15}$ K cm$^2$
for the mean-field parameter of H-$^3$He interaction in 2D. The experiments
were carried out with overall $^3$He concentrations ranging from 0.1 ppm to 5 %
as well as with commercial and isotopically purified $^4$He at temperatures
70...400 mK. Measuring by ESR the rate constants $K_{aa}$ and $K_{ab}$ for
second-order recombination of hydrogen atoms in hyperfine states $a$ and $b$ we
find the ratio $K_{ab}/K_{aa}$ to be independent of the $^3$He content and to
grow with temperature.
