Perforated bilayers play an essential role in biology and in surface science. Here, we extend the classical aggregation model of catanionic surfactant mixtures to describe perforations in a self-assembled bilayer in aqueous salt. The model predicts that changing solution salinity and anionic-to-cationic surfactant ratio may lead to the spontaneous formation of pores in the bilayer and to the assembly of a micellar network. We estimate the dimensions of an optimal pore as a function of solution salinity and aggregate composition and show that with an increase of concentration of the deficient surfactant in a catanionic mixture, both the diameter and the thickness of the optimal pore decrease. This decrease is stronger for pores enriched in surfactant having a longer tail than for the pores enriched in the oppositely charged surfactant with a shorter tail. Our model helps to quantify the driving forces for the formation of a pore in a catanionic bilayer and to understand its role. For the aqueous mixtures C16TAB/SOS/NaBr and DTAB/SDS/NaBr, our predictions are in reasonable although not quantitative agreement with available cryo-TEM and SANS data. Predicted radii of perforations are in the range of those obtained from SANS
data for perforated bilayer disks.