A coarse-grain model for amphiphilic diblock copolymers is developed by fitting the required parameters to properties taken from all-atom molecular dynamics simulations and experimental data. Computations with the present coarse-grain model yield spontaneous self-assembly of a random system into membrane bilayers when the amphiphilic diblock copolymers have a lipid-like hydrophilic/hydrophobic ratio. The model semiquantitatively reproduces a number of experimental results that were not explicitly used in the parametrization. In particular, diblock polymers with the appropriate ratio of hydrophobic - hydrophilic segment lengths self-assemble into membranes whose hydrophobic thickness (determined from mass density profiles) and scaling with molecular weight are found to be in good agreement with the experiment.