We study the interplay between thermal undulations and electrostatic interactions for weakly charged surfactant bilayers by measuring the backscattering of light from very dilute lamellar phases of the non-ionic surfactant triethylene glycol monodecyl ether (C10E3) doped with small amounts of the anionic surfactant sodium dodecyl sulphate (SDS), both with and without added electrolyte. Upon charging, the lamellar phases show a transition from undulation to electrostatic stabilization. Non-lamellar structures develop if the molar mixing ratio R = [SDS]/[C10E3] exceeds ≈ 2.5 × 10 −3 . Deviations from ideal swelling, D ∝ 1/Φ, whereD is the lamellar repeating distance and Φ the membrane volume fraction, were detected for all lamellar phases. Salt-free lamellar phases with charge densities below σc = 1.47 × 10 −4 e/nm 2 , as well as more highly charged lamellar phases at high ionic strength show a universal logarithmic deviation from ideal swelling that was analyzed using theories for undulation stabilized lamellar phases. Deviations from ideal swelling for electrostatically stabilized lamellar phases were analyzed using theories recently developed for undulations in charged lamellar phases. The fits to the various theories yield a value of kc,0 ≈ 1.8 kBT for the bending modulus of the C10E3 bilayers. PACS. 82.70.-y Disperse systems -61.30.Eb Experimental determinations of smectic, nematic, cholesteric, and other structures -68.10.-m Fluid surfaces and fluid-fluid interfaces