Polyethylene (PE) and isotactic polypropylene (iPP) constitute nearly two-thirds of the world’s plastic. Despite their similar hydrocarbon makeup, the polymers are immiscible with one another. Thus, common grades of PE and iPP do not adhere or blend, creating challenges for recycling these materials. We synthesized PE/iPP multiblock copolymers using an isoselective alkene polymerization initiator. These polymers can weld common grades of commercial PE and iPP together, depending on the molecular weights and architecture of the block copolymers. Interfacial compatibilization of phase-separated PE and iPP with tetrablock copolymers enables morphological control, transforming brittle materials into mechanically tough blends.