The music site Magnatune (http://magnatune.com) does that.
They split your money into two piles, one for downloading (you can download anything you want) and one for streaming.
Having just superficially perused Magnatune's info pages, I couldn't find anything specifying how they determine the amount given to artists, other than 50% of it goes to artists, and the other 50% goes to Magnatune...