Prolonged disposal of organic and inorganic waste in shallow land burial sites throughout the USA has prompted detailed investigations of subsurface contaminant transport processes. The fate and transport of contaminant leakage from pits, trenches, and cribs into the vadose zone via storm events is not well understood. The objective of this study was to investigate the thermodynamic and kinetic processes controlling the transport of inorganic contaminants in unsaturated, heterogeneous subsurface media. Large undisturbed columns were isolated from a proposed waste site consisting of fractured saprolite (weathered interbedded shale and limestone), and steady‐state nonreactive and reactive solute transport experiments were performed at a variety of pressure heads. Observed breaktbrough curves (BTC) for binary and ternary mixtures in the Co‐Sr‐Ca system were delayed relative to nonreactive Br BTC, indicating that the former tracers were adsorbed by the solid phase. Transport of the binary mixtures Co‐Ca and Sr‐Ca was predicted reasonably well with the equilibrium convective‐dispersive (CD) equation using independent measurements of all model parameters. However, application of the nonequilibrium or kinetic CD model to the observed Sr and Co binary data resulted in an improved description of contaminant transport. Cation‐exchange equilibria relationships on homogenized subsurface material, using both shake batch and miscible displacement methods, adequately described the thermodynamic processes that were prevalent during contaminant transport. These results suggest that preferential transport of reactive contaminants is negligible for the unsaturated conditions used in this study, and that the structured saprolite within the subsurface media is a chemically active constituent during reactive solute transport. Although the transport of contaminants in the ternary Co‐Sr‐Ca system exhibited many of the same features as the binary transport studies, an attempt to simulate the transport of contaminants in the ternary system as independent species was less than adequate.