Cocontinuous blends were prepared from polyethylene (PE) and polylactic acid (PLA). The extensional and shear rheological properties of PE and PLA were independently tuned by varying long chain branching architecture. Shear rheological properties of the blend components were characterized by capillary and oscillatory rheometry. Extensional rheological properties were characterized by orifice entrance pressure drop and sheet wind-up. It was found that branching significantly increased zero-shear viscosity and extensional viscosity, but did not alter the shear viscosity at the shear rates typically observed in mixing flows. Adding a branched polymer to the blend allowed the other blend component to percolate into a continuous network with less material. Blending with two branched materials significantly broadened the range of cocontinuous compositions from 39-59 vol. % with a linear/linear blend to 25-76 vol. % for a branched/branched blend. This was attributed to the ability of a strain hardening matrix to promote elongation, and hence percolation, of the minor phase. Domain size was minimized when a slight amount of strain hardening was introduced, as this allowed formation of narrow features while stabilizing them against fiber breakup. All blends showed a rate of morphological coarsening during annealing inversely proportional to zero-shear rate viscosity, suggesting that quiescent coarsening flows are dictated by low-rate shear flow properties and not extensional properties. We find that our results and coarsening rates in the literature show the same linear dependence on the ratio of interfacial tension to log volume average zero-shear viscosity with a coefficient of ∼0.03, indicating a simple universal relation.