With an annual production of hundreds of millions of tons, the few commodity polymers that dominate the plastics market cannot satisfy all the applications and expectations. In this context, the fabrication of thermodynamically stable polymer blends structured on submicrometre scales raises much hope, but poses significant scientific and industrial challenges. Here, we propose and demonstrate for an industrially relevant system, polyethylene and polyamide, that hitherto inaccessible co-continuous morphologies can be produced over a wide range of compositions by reactive blending. Paradoxically, the self-assembled structures are thermodynamically stable because of the molecular polydispersity inherent in the production method. These nanostructured materials present a unique combination of properties impossible to achieve with classical blends. This versatile, low-cost and simple strategy should be widely applicable.