Extensive molecular dynamics (MD) simulations of binary systems of phospholipids and bile salts, a model for human bile, have been performed. Recent progress in hardware and software development allows simulation of the spontaneous aggregation of the constituents into small mixed micelles, in agreement with experimental observations. The MD simulations reveal the structure of these micelles at atomic detail. The phospholipids are packed radially with their headgroups at the surface and the hydrophobic tails pointing toward the micellar center. The bile salts act as wedges between the phospholipid headgroups, with their hydrophilic sides exposed to the aqueous environment. The structure of the micelles strongly resembles the previously proposed radial shell model. Simulations including small fractions of cholesterol reveal how cholesterol is solubilized inside these mixed micelles without changing their overall structure.