Positron lifetime measurements have been made on BHDC/water/benzene microemulsions, at different water to surfactant molar ratios (w(0)) and different surfactant concentrations (C-BHDC). Recently, a model has been proposed to explain the positronium formation and annihilation in AOT/water/isooctane microemulsions, which states that the majority of positronium. formation occurs in the aqueous cores of the reverse micelles, and the o-Ps there formed diffuses out of the aqueous cores into the organic solvent bulk. The BHDC based microemulsion system has been chosen in order to study the influence of the cationic head group and of the chloride counterion present in the aqueous pseudophase on the Ps formation probability and on the o-Ps diffusion out of the aqueous cores. The results of this study are satisfactorily explained by the referred model. The radii of the aqueous cores for different w(0) values and calculated from the o-Ps lifetime measurements, are in good agreement with the values reported in the literature. The measured o-Ps intensities in both the aqueous pseudophase and the organic phase were found to be in agreement with those calculated by taking into account the partial inhibition due to the chloride counterions present in the aqueous cores.