We report an investigation of the lamellar phase of the system N,N-dimethyldodecylamine oxide (DDAO)/ gramicidin D/water. To identify the dominant repulsive interaction between the gramicidin-crammed membranes, we measured the variation (with the membrane volume fraction) of the position of the Bragg peaks in an X-ray diffraction experiment and the H-2 NMR quadrupolar splitting of heavy water and of alpha-deuterated DDAO. Though none of the components are ionic, the results are consistent with an electrostatically stabilized lamellar phase with a low surface charge density (<10(-4) C/m(2)). The surface charge is likely due to either ionic impurities, that bind to the mouth of the gramicidin channel, or partial protonation of DDAO in the membrane. It was also possible to determine the membrane bending rigidity to be in the range kappa = 5-10k(B)T.