We report the collapse of an electrostatically swollen surfactant lamellar phase above a critical concentration of an added nonionic surfactant due to hydrogen bonding between the two types of headgroups. At still higher concentrations of the neutral surfactant a temperature-driven lamellar to coacervate transition is observed. Small-angle X-ray diffraction pattern of the coacervate can be modeled as arising from bilayers with short-range positional correlations, whereas cryo-scanning electron microscopy images show bilayer-like features riddled with pores. Very similar behavior is found when the nonionic polyoxyethylene alkyl ether surfactant is replaced by polyethylene glycol of sufficiently high molecular weight.