Localization of nanoparticles at the interface of cocontinuous blends provides a way to enhance polymer blend properties as well as prepare surface-modified porous materials (via removal of one blend component). In this study, we systematically investigate kinetic and thermodynamic control of interfacial localization of silica nanoparticles (SNPs) in cocontinuous blends of polypropylene (PP) and ethylene vinyl acetate (EVA). By changing the order of addition of blend components and shortening the blending time, we demonstrate that bare SNPs (without any surface functionalization) are kinetically arrested at the interface of PP/EVA cocontinuous structures. This kinetically driven arrest is further shown to be comparable in morphology and rheological properties of blends prepared with surface-functionalized SNPs, which are thermodynamically driven to pin the interface. Two-channel confocal fluorescence microscopy is utilized to study the effect of particle functionalization, melt-compounding sequence, and mixing times on the morphology of the cocontinuous blends. We estimate the degree of interface-localized silica by spatial variation of the SNP channel fluorescence intensity across the phase domains. A direct relation between the initial interfacial localization of particles after blending, blend storage modulus, and the characteristic length evolution during coarsening was demonstrated for SNP-stabilized cocontinuous blends. We find that a similar relation holds regardless if the particles are trapped kinetically or thermodynamically at the interface. These results present a direct, quantitative, experimental demonstration of the association between the particle interfacial localization and rheological and morphological properties of the cocontinuous blends and demonstrate the broader premise of deriving surface-modified porous materials without any tuning of particle properties.