Mid-infrared absorption spectroscopy has been used extensively to study the molecular properties of cell membranes and model systems. Most of these studies have been carried out on macroscopic samples or on samples a few micrometers in size, due to constraints on sensitivity and spatial resolution with conventional instruments that rely on far-field optics. Properties of membranes on the scale of nanometers, such as in-plane heterogeneity, have to date eluded investigation by this technique. In the present work, we demonstrate the capability to study single bilayers of phospholipids with near-field mid-infrared spectroscopy and imaging and achieve a spatial resolution of at least 40 nm, corresponding to a sample size of the order of a thousand molecules. The quality of the data and the observed spectral features are consistent with those reported from measurements of macroscopic samples and allow detailed analysis of molecular properties, including orientation and ordering of phospholipids. The work opens the way to the nanoscale characterization of the biological membranes for which phospholipid bilayers serve as a model.