We present a novel method to measure and to analyze lipid bilayer fluctuations based on time-of-flight nonspecular neutron reflectivity (TOF-NSNR). To validate this approach, we compare the results obtained on the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) to NSNR data collected in the conventional monochromatic mode. For the DMPC model system in its fluid L-alpha phase, we determine the fluctuation spectrum of an averaged bilayer in an oriented multilamellar stack and compare the result to the predictions of the linearized smectic free energy functional. In particular, we show how the smectic penetration depth Lambda can be determined from the measurements. Furthermore, significant changes in the fluctuation spectrum of DMPC are observed upon the interaction with the antimicrobial peptide magainin 2 and cannot be explained by the smectic model.