Methods for demulsifying an emulsified petroleum source having a predetermined resin-to-asphaltene ratio without substantial aggregation or precipitation of asphaltenes may include adding a resin supplement to the emulsified petroleum source to form a resin-supplemented emulsion having a resin-to-asphaltene ratio above a predetermined critical value. An acidic-to-basic ratio of acidic functional groups to basic functional groups in the supplemented emulsion may be adjusted to be from about 0.25 to about 4.0. The resin-supplemented emulsion may be contacted with carbon dioxide to form an initial mixture having an emulsified oil phase and an emulsified aqueous phase. The initial mixture may be stabilized to facilitate rupture of the resin-supplemented emulsion, to cause phase separation, and to allow removal of a separated oil phase. The resin-to-asphaltene ratio being above the predetermined critical value in the supplemented emulsion maintains asphaltene suspension during demulsification, such that asphaltene agglomeration and precipitation are avoided.