Mixtures of cationic lipids and DNA can form tight complexes that have the potential to act as vectors for gene delivery into cells. These complexes can have a range of different morphologies, which depend upon factors including the lipid type and hydration level. As the efficiency of the complex as a gene delivery vector is tightly coupled to its morphology, understanding how the different phases form is crucial for future development of efficient vectors. We have adapted the MARTINI force field developed by Siewert-Jan Marrink to create a coarse-grained model of DNA. This model is used to study the interaction of zwitterionic and cationic phospholipids with DNA via molecular dynamics simulation. Some recent results as well as future work in terms of DNA model refinement will be discussed.