A method of drilling a subterranean formation includes providing an invert emulsion fluid comprising an oleaginous continuous phase; an internal phase comprising water; bentonite; and mixed metal layered hydroxides comprising hydroxide ions associated with at least two metal cations wherein one is divalent and another is trivalent; and drilling the subterranean formation with the drilling fluid. Invert emulsion drilling fluids include an oleaginous continuous phase; an internal phase comprising water; sodium bentonite; and mixed metal layered hydroxides comprising hydroxide ions associated with at least two metal cations.