•Cavitation bubble dynamics in the vicinity of liquid-liquid interface was studied.•Advanced simulations were used to interpret the experimental observations.•Dependence of the bubble jetting to the anisotropy parameter was investigated.•The study has a great applied value in the field of ultrasonic emulsification. The initial motivation for the study was to gain deeper understanding into the background of emulsion preparation by ultrasound (cavitation). In our previous work (Perdih et al., 2019) we observed rich phenomena occurring near the liquid-liquid interface which was exposed to ultrasonic cavitation. Although numerous studies of bubble dynamics in different environments (presence of free surface, solid body, shear flow and even variable gravity field) exist, one can find almost no reports on the interaction of a bubble with a liquid-liquid interface. In the present work we conducted a number of experiments where single cavitation bubble dynamics was observed on each side of the oil-water interface. These were accompanied by corresponding simulations. We investigated the details of bubble interface interaction (deformation, penetration). As predicted, by the anisotropy parameter the bubble always jets toward the interface if it grows in the lighter liquid and correspondingly away from the interface if it is initiated inside the denser liquid. We extended the analysis to the relationships of various bubble characteristics and the anisotropy parameter. Finally, based on the present and our previous study (Perdih et al., 2019), we offer new insights into the physics of ultrasonic emulsification process.