In this contribution, we use dissipative particle dynamics simulations to investigate the orientations of lamella-forming copolymers with two blocks of equal molecular weight confined in thin films. We employ neutral and symmetric interactions between the copolymer blocks and the walls, a situation for which contradicting observations have been made in experiments and previous theoretical studies. Our model takes into account a realistic degree of conformational asymmetry between the blocks, which stems from unequal Kuhn lengths of the constituent monomers. We perform a thorough scaling analysis to exclude finite size effects, and find, in agreement with experiments, a remarkable cascade of morphological transitions from parallel to perpendicular orientations when the film height is varied. We demonstrate that the emergence of a stable parallel configuration stems from entropic effects due to the conformational asymmetry and the confinement of the system.