Biological membranes are highly organized supra- molecular assemblies of lipids and proteins. The membrane interface separates the outer (bulk) aqueous phase from the hydrophobic membrane interior. In this work, we have explored the microstructure and collective dynamics of the membrane interfacial hydration shell in zwitterionic and negatively charged phospholipid membrane bilayers using terahertz time-domain spectroscopy. We show here that the relaxation time constants of the water hydrogen bond network exhibit a unique "rise and dip" pattern with increasing lipid concentration. More importantly, we observed a dependence of the critical lipid concentration corresponding to the inflection point on the charge of the lipid headgroup, thereby implicating membrane electrostatics as a major factor in the microstructure and dynamics of water at the membrane interface. These results constitute one of the first experimental evidences of the modulation of the dielectric relaxation response of membrane interfacial water by membrane lipid composition in a concentration-dependent manner. Lipid-stringent membrane hydration could be relevant in the broader context of lipid diversity observed in biological membranes and the role of negatively charged lipids in membrane protein structure and function.