Biomimetic polymer/protein membranes are promising materials for DNA sequencing, sensors, drug delivery and water purification. These self-assembled structures are made from low molecular weight amphiphilic block copolymers (Nhydrophobic < 40 for a diblock copolymer), including poly(ethylene oxide)-1,2-polybutadiene (EO-1,2-BD) and poly(ethylene oxide)-poly(ethyl ethylene) (EO-EE). To examine these membranes' nanoscale structure, we developed a coarse-grained molecular dynamics (CG MD) model for EO-1,2-BD and assembled a CG MD model for EO-EE using parameters from two published force fields. We observe that the polymers' hydrophobic core blocks are slightly stretched compared to the random coil configuration seen at higher molecular weights. We also observe an increase in the interdigitation of the hydrophobic leaflets with increasing molecular weight (consistent with literature). The hydration level of the EO corona (which may influence protein incorporation) is higher for membranes with a larger area/chain, regardless of whether EE or 1,2-BD forms the hydrophobic block. Our results provide a molecular-scale view of membrane packing and hydrophobicity, two important properties for creating polymer-protein biomimetic membranes.