The erosion of amorphous hydrocarbon films by bombardment with argon ions and simultaneous exposure to thermal atomic hydrogen is studied as a function of ion energy and hydrogen/argon flux ratio by molecular dynamics simulations using a reactive hydrocarbon potential and compared with experimental data. While erosion due to energetic argon only is dominated by physical sputtering, the additional presence of atomic hydrogen leads to a marked increase of erosion. The erosion yield increases with both hydrogen/argon flux ratio and energy. A mechanism has been identified which explains the experimentally observed increase of the sputtering yield for simultaneous bombardment: the surface erosion induced by momentum transfer processes is enhanced by screening effects of the additionally offered hydrogen in the near-surface region.