The transfer rate of a probe molecule across the interfacial layer of a water-in-oil (w/o) microemulsion was investigated using a combination of transverse field muon spin rotation (TF-mu SR), avoided level crossing muon spin resonance (ALC-mu SR), and Monte Carlo simulations. Reverse micro emulsions consist of nanometer-sized water droplets dispersed in an apolar solvent separated by a surfactant monolayer. Although the thermodynamic, static model of these systems has been well described, our understanding of their dynamics is currently incomplete. For example, what is the rate of solute transfer between the aqueous and apolar solvents, and how this is influenced by the structure of the interface? With an appropriate choice of system and probe molecule, mu SR offers a unique opportunity to directly probe these interfacial transfer dynamics. Here, we have employed a well characterized w/o microemulsion stabilized by bis(2-ethylhexyl) sodium sulfosuccinate (Aerosol OT), with allyl alcohol (CH2=CH-CH2-OH, AA) as the probe. Resonances due to both muoniated radicals, CMuH(2)-C*H-CH2-OH and C*H-2-CHMu-CH2-OH, were observed with the former being the dominant species. All resonances displayed solvent dependence, with those in the microemulsion observed as a single resonance located at intermediate magnetic fields to those present in either of the pure solvents. Observation of a single resonance is strong evidence for interfacial transfer being in the fast exchange limit. Monte Carlo calculations of the Delta M = 0 ALC resonances are consistent with the experimental data, indicating exchange rates greater than 10(9) s(-1), placing the rate of interfacial transfer at the diffusion limit.