We investigated the properties of 1-decyl-3-methylimidazolium bromide (DMImBr), a molten salt at room temperature, and its mixtures with water in the whole proportions. At low concentrations, this salt behaved like a classical cationic amphiphile. Its critical micellar concentration (cmc) was determined by conductimetry and by measuring electromotive forces (EMF) with bromide or cationic surfactant-selective electrodes. Moreover, the association rate of the counter ion to micelle has been determined on a wide range of concentrations, allowing characterising the micellisation equilibrium by a solubility product. The conductivity of this liquid electrolyte in mixtures with water was maximal at high concentrations. We modelled this behaviour, taking into account the molar volume fraction of both phases. Our results show that these solutions, which are composed of dispersed aggregates, behave like mixtures of two phases that interpenetrate themselves.