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The lateral diffusion and trapping of protein receptors within the postsynaptic membrane of a neuron plays a key role in determining the strength of synaptic connections and their regulation during learning and memory. In this paper we construct and analyze a 2D interfacial diffusion model of inhibitory synaptic receptor dynamics. The model involves three major components. First, the boundary of each synapse is treated as a semi-permeable interface due to the effects of cytoskeletal structures. Second, the effective diffusivity within a synapse is taken to be smaller than the extrasynaptic diffusivity due to the temporary binding to scaffold protein buffers within the synapse. Third, receptors from intracellular pools are inserted into the membrane extrasynaptically and internalized extrasynaptically and synaptically. We first solve the model equations for a single synapse in an unbounded domain and explore how the non-equilibrium steady-state number of synaptic receptors depends on model parameters. We then use matched asymptotic analysis to solve the corresponding problem of multiple synapses in a large, bounded domain. Finally, treating a synapse as a phase separated condensate of scaffold proteins, we describe how diffusion of individual scaffold proteins can also be modeled in terms of interfacial diffusion. We thus establish interfacial diffusion as a general paradigm for exploring synaptic dynamics and plasticity.