Reversible emulsification drilling fluids can achieve conversion between oil-based drilling fluids and water-based drilling fluids at different stages of drilling and completion, combining the advantages of both to achieve the desired drilling and completion effects. The foundation of reversible emulsion drilling fluids lies in reversible emulsions, and the core of a reversible emulsion is the reversible emulsifier. In this study, we prepared a reversible emulsifier, DMOB(N,N-dimethyl-N′-oleic acid-1,4-butanediamine), and investigated the reversible phase inversion process of reversible emulsions, including the changes in the reversible emulsifier (HLB) and its distribution at the oil–water interface (zeta potential). From the perspective of the acid–alkali response mechanism of reversible emulsifiers, we explored the reversible phase inversion mechanism of reversible emulsions and reversible emulsification drilling fluids. It was revealed that the reversible phase inversion of emulsions could be achieved by adjusting the pH of the emulsion system. Then the proportion of ionic surfactants changed in the oil–water interface and subsequently raised/lowered the HLB value of the composite emulsifier at the oil–water interface, leading to reversible phase inversion of the emulsion. The introduction of organic clays into reversible emulsification drilling fluid can affect the reversible conversion performance of the drilling fluids at the oil–water interface. Thus, we also investigated the influence of organic clays on reversible emulsions. It was demonstrated that a dosage of organic clay of ≤2.50 g/100 mL could maintain the reversible phase inversion performance of reversible emulsions. By analyzing the microstructure of the emulsion and the complex oil–water interface, we revealed the mechanism of the influence of organic clay on the reversible emulsion. Organic clay distributed at the oil–water interface not only formed a complex emulsifier with surfactants, but also affected the microstructure of the emulsion, resulting in a difficult acid-induced phase transition, an easy alkali-induced phase transition, and improved overall stability.