The objective of this contribution is to investigate the role of generalized interfaces in the overall response ofparticulate composites and the associated size effects. Throughout this work, the effective properties of com-posites are obtained via three-dimensional computational simulations using the interface-enhancedfinite ele-ment method for a broad range of parameters. The term interface corresponds to a zero-thickness model re-presenting the interphase region between the constituents and accounting for the interfaces at the micro-scaleintroduces a physical length-scale to the effective behavior of composites, unlike the classicalfirst-orderhomogenization that is missing a length-scale. The interface model here is general in the sense that both tractionand displacement jumps across the interface are admissible recovering both the cohesive and elastic interfacemodels. Via a comprehensive computational study, we identify extraordinary and uncommon characteristics ofparticle reinforced composites endowed with interfaces. Notably, we introduce the notion ofcritical sizeat whichthe overall behavior, somewhat surprisingly, shows no sensitivity with respect to the inclusion-to-matrix stiffnessratio. Our study, provides significant insight towards computational design of composites accounting for in-terfaces and in particular, nano-composites.