In order to investigate experimentally inaccessible, molecular-level detail regarding interleaflet interaction in membranes, we have run an extensive series of coarse-grained molecular dynamics simulations of phase separated lipid bilayers. The simulations are motivated by differences in lipid and cholesterol composition in the inner and outer leaflets of biological membranes. Over the past several years, this phenomenon has inspired a series of experiments in model membrane systems which have explored the effects of lipid compositional asymmetry in the two leaflets. The simulations are directed at understanding one potential consequence of compositional asymmetry, that being regions of bilayers where liquid-ordered (Lo) domains in one leaflet are opposite liquid-disordered (Ld) domains in the other leaflet (phase asymmetry). The simulated bilayers are of two sorts: 1) Compositionally symmetric leaflets where each of the two leaflets contains an identical, phase separated (Lo/Ld) mixture of cholesterol, saturated and unsaturated phospholipid; and 2) Compositionally asymmetric leaflets, where one leaflet contains a phase separated (Lo/Ld) mixture while the other contains only unsaturated lipid, which on its own would be in the Ld phase. In addition, we have run simulations where the lengths of the saturated lipid chains as well as the mole ratios of the three lipid components are varied. Collectively, we report on three types of interleaflet coupling within a bilayer. First, we show the effects of compositional asymmetry on acyl chain tilt and order, lipid rotational dynamics, and lateral diffusion in regions of leaflets that are opposite Lo domains. Second, we show substantial effects of compositional asymmetry on local bilayer curvature, with the conclusion that phase separated leaflets resist curvature, while inducing large degrees of curvature in an opposing Ld leaflet. Finally, in compositionally symmetric, phase separated bilayers, we find phase asymmetry (domain antiregistration) between the two leaflets occurs as a consequence of mismatched acyl chain-lengths in the saturated and unsaturated lipids.