We apply the self-consistent field (SCF) theory for chain molecules in inhomogeneous systems, originated by Scheutjens and Fleer, to study the interaction between two water droplets in oil in the presence of surfactants. The modelling of interacting polymer-covered rigid interfaces is the classical application in the SCF approach. In this paper we study two surfactant-covered liquid-liquid interfaces near contact. This can be done by an osmotic pressure 'experiment'. Our analysis indicates that for (surfactant-stabilised) water-in-oil emulsions two types of colloidal instability can be distinguished: (1) coalescence (flocculation in the primary minimum leading to a reduction of the number of droplets) and (2) aggregation (flocculation in secondary minimum, formation of clusters of droplets, i.e. a reduction of the number of kinetically active droplets but retaining their individuality). The surfactant adsorbed at the water-oil interface influences these two types of instabilities in different ways. A high surfactant concentration effectively protects against coalescence, whereas, especially when the molecular weight of the oil molecules is larger than that of the surfactants, aggregation is promoted. Analysis of the interaction curves for lamellar interfaces enables the prediction of the macroscopic contact angle between two droplets. We show that this angle can vary strongly with the type of oil used. Protection against aggregation can be obtained by carefully choosing the surfactant in connection with the oil used.