Abstract: According to an embodiment, an invert emulsion drilling fluid comprises: an external phase, wherein the external phase of the drilling fluid comprises a hydrocarbon liquid; an internal phase, wherein the internal phase of the drilling fluid comprises a hygroscopic liquid; and a suspending agent, wherein the suspending agent is a polymer comprising urea linkages or urea and urethane linkages. According to certain embodiments, the hygroscopic liquid comprises a salt and a suitable solvent. According to other embodiments, the hygroscopic liquid comprises an alcohol. In certain embodiments, the drilling fluid does not contain an organophilic clay or organophilic lignite. According to another embodiment, a method of using the invert emulsion drilling fluid comprises: introducing the drilling fluid into at least a portion of a subterranean formation.