We describe an approach to prepare co-continuous microstructured blends of polymers and nanoparticles by formation of a percolating network of particles within one phase of a polymer mixture undergoing spinodal decomposition. Nanorods or nanospheres of CdSe were added to near-critical blends of polystyrene and poly(vinyl methyl ether) quenched to above their lower critical solution temperature. Beyond a critical loading of nanoparticles, phase separation is arrested due to the aggregation of particles into a network (or colloidal gel) within the poly(vinyl methyl ether) phase, yielding a co-continuous spinodal-like structure with a characteristic length scale of several micrometers. The critical concentration of nanorods to achieve kinetic arrest is found to be smaller than for nanospheres, which is in qualitative agreement with the expected dependence of the nanoparticle percolation threshold on aspect ratio. Compared to structural arrest by interfacial jamming, our approach avoids the necessity for neutral wetting of particles by the two phases, providing a general pathway to co-continuous micro- and nanoscopic structures.