A concise review is provided of fundamentals of interfacial transport and rheology, which includes simple proofs of the surface divergence theorem and the surface Reynolds transport theorem, needed in the derivations. The results are applied to the prototype example of a dilute emulsion of spherical drops suspended in an immiscible continuous fluid, in the circumstance where the interface separating the two phases possesses its own rheological properties (i.e., surface shear and dilatational viscosities). The low-Reynolds-number hydrodynamics of the emulsion droplets in a general linear flow is analyzed using invariant methods, providing the velocity, pressure and stress fields everywhere and allowing the leading order deformation of the drops to be calculated. The average stress in the dilute emulsion is also obtained to first order in the volume fraction of the dispersed phase. The results suggest that simultaneous measurements of the effective viscosity of the emulsion and the deformation of the drops in a linear shear flow can provide an indirect experimental determination of the surface shear and dilatational viscosities.