Interaction of DNA with zwitterionic phospholipids is an important long-standing problem in the field of liposome-based gene delivery. Although it is well-established that divalent cations can promote formation of stable DNA-phospholipid complexes, the underlying molecular mechanism remains largely unknown. Here we employ computer simulations to gain atomistically resolved insight into the kinetics of calcium-induced adsorption of DNA on zwitterionic phosphatidylcholine membranes as well as into the structure and stability of the resulting complexes. Overall, our findings show that calcium ions play a dual role in DNA-phospholipid systems. First, binding of divalent cations to the lipid-water interface turns the surface of the zwitterionic membrane positively charged, promoting thereby the initial electrostatic attraction of a polyanionic DNA molecule. Second, we show that calcium ions are crucial for stabilizing the DNA-lipid membrane complex as they bridge together phosphate groups of DNA and lipid molecules. In contrast to previous hypotheses, we demonstrate that direct interactions between choline groups of phospholipids and DNA phosphates play only a rudimentary role as they are relatively short-lived and unstable: typical residence times for such interactions are 2 orders of magnitude smaller than those for Ca-mediated bridges between DNA and lipid phosphate groups. The results of our study can serve as a basis for a deeper understanding of molecular mechanisms behind noncovalent binding of DNA and DNA-based nanodevices to complex surfaces such as cell membranes.