One of the potentially most important issues in accurately modeling directed self-assembly of block copolymers (BCPs) is the fact that the real BCPs often have block energy and/or density asymmetry, meaning that each block has a different homopolymer density and/or cohesive energy density (CED). A simulation of BCP behavior based on molecular dynamics of coarse-grained polymer chains has been developed that can independently parameterize and control the density and the CED of each block to more accurately match this asymmetry. This model was used to study the effect on the order-disorder transition (ODT), domain scaling, and self-assembly of thin films of BCPs. BCPs whose blocks each have a different density show deviations from the mean-field ODT coexistence curve, exhibiting an asymmetric order-disorder transition curve. Self-assembly of thin films of BCPs with mismatches in CED shows significant changes in morphologies compared to BCPs with energetically symmetric blocks, because the lowest CED block has a strong propensity to segregate to and “wet” the free interface. This CED mismatch also gives rise to a large number of deviations from bulk behavior including changing vertical-to-horizontal morphologies through film depth, compression and expansion of domain sizes, and island and hole formations among others.