The present application discloses drilling fluid compositions, methods for making drilling fluids, and methods for drilling subterranean wells utilizing the drilling fluids. According to one embodiment, a drilling fluid composition may include an oil phase, an aqueous phase, an emulsifier, and a rheology modifier. The emulsifier may include an amino amide, and the rheology modifier may include a layered double hydroxide, such as Mg/Al-Myristate layered double hydroxide.