It is now widely acknowledged that continuous oil-spreading films observed in 2D glass-micromodel studies for strongly water-wet three-phase oil, water, and gas systems are also present in real porous media, and they result in lower tertiary-gasflood residual oil saturations than for corresponding negative spreading systems that do not display oil-spreading behavior. However, it has not yet been possible to directly confirm the presence of continuous spreading films in real porous media in three dimensions, and little is understood of the distribution of the phases within the complex geometry and topology of actual porous media for different spreading conditions. This paper describes a study with high-resolution X-ray microtomography to image the distribution of oil, water, and gas after tertiary gasflooding to recover waterflood residual oil for two sets of fluids, one positive spreading and the other negative spreading, in strongly water-wet Bentheimer sandstone. We show that, for the positive spreading system, oil-spreading films maintain the connectivity of the oil phase down to low oil saturation. At similar oil saturation, no oil films are observed for the negative spreading system, and the oil phase is disconnected. The spatial continuity of the oil-spreading films over the imaged volume is confirmed by the computed Euler characteristic for the oil phase.