In this paper, we investigate the two mechanisms that are responsible for the release of a chemical substance from water-in-oil-in-water double emulsions. (i) One is due to the coalescence of the thin liquid film separating the internal droplets and the oil globule surface. (ii) The other mechanism occurs without film rupturing, that is, by diffusion and/or permeation of the chemical substance across the oil phase. The thin liquid film that forms between the internal droplets and the globule surface is composed of two mixed monolayers covered by hydrophilic and hydrophobic surfactant molecules. Following the well-known Bancroft rule, such inverted films possess a long-range stability with respect to coalescence when essentially covered by hydrophobic surfactant. In that limit, the release is governed by diffusion and/or permeation. However, the film becomes very unstable when a strong proportion of hydrophilic surfactant is adsorbed and the release is then controlled by coalescence. We show that the transition from one regime (diffusion) to the other (coalescence) may be achieved by varying the concentration of the hydrophilic surfactant in the external water phase. We study the kinetics of release in the regime dominated by coalescence, and we propose an unambiguous method for the measurement of the microscopic parameters implied in liquid film rupturing. Our method exploits the fact that the total number of internal droplets adsorbed on the globule surface governs the rate of release. At low internal droplet volume fraction, measuring the rate of release allows a direct determination of the average lifetime of the thin film that forms between the small internal droplet and the globule surface. We deduce the activation energy and the natural frequency of the coalescence process by exploring the temperature dependence of the rate of release.