Hybrid membranes assembled from biological lipids and synthetic polymers are a promising scaffold for the reconstitution and utilization of membrane proteins. Recent observations indicate that inclusion of small fractions of polymer in lipid membranes can improve protein folding and function, but the exact structural and physical changes a given polymer sequence imparts on a membrane often remain unclear. Here, we use all-atom molecular dynamics simulations to study the structure of hybrid membranes assembled from DOPC phospholipids and PEO-b-PBD diblock copolymers. We verified our computational model using new and existing experimental data and obtained a detailed picture of the polymer conformations in the lipid membrane that we can relate to changes in membrane elastic properties. We find that inclusion of low polymer fractions induces transient packing defects into the membrane. These packing defects act as insertion sites for two model peptides, and in this way, small amounts of polymer content in lipid membranes can lead to large increases in peptide insertion rates. Additionally, we report the peptide conformational space in both pure lipid and hybrid membranes. Both membranes support similar alpha helical peptide structures, exemplifying the biocompatibility of hybrid membranes.