We present here results on the transfer kinetics of monoglyceride and n-alkanes in water. Transfer kinetics between cubosomes and emulsion droplets were followed using time-resolved small-angle X-ray scattering measurements, while dynamic light scattering was used to study the changes in the particle radii. The effect of the initial size of cubosomes and emulsion droplets on the final droplet size of the mixed components was investigated. Decane was transferred into the cubosomes with the disappearance of all emulsion droplets, with no detectable transfer of monoglyceride. Cubosomes were even found to absorb bulk decane into the solution from a surface layer, which raises the possibility of using cubosomes to bind hydrophobic molecules from the bulk phase. In mixtures with longer alkanes, transfer of both monoglyceride and oil was observed; while with octadecane the transfer of monoglyceride into emulsion droplets dominated. Calculating the point at which the transfer of monoglyceride becomes dominant over that of oil as the alkane chain length is increased shows that, in compositional ripening, monoglyceride behaves as an alkane with 15.3 carbons. These results further our understanding of the interactions of internally self-assembled particles in various media and suggest possible ways of controlling the size of the particles.