A search for supersymmetry through the direct pair production of top squarks, with Higgs (H) or Z bosons in the decay chain, is performed using a data sample of proton–proton collisions at s=8TeV collected in 2012 with the CMS detector at the LHC. The sample corresponds to an integrated luminosity of 19.5 fb−1. The search is performed using a selection of events containing leptons and bottom-quark jets. No evidence for a significant excess of events over the standard model background prediction is observed. The results are interpreted in the context of simplified supersymmetric models with pair production of a heavier top-squark mass eigenstate t˜2 decaying to a lighter top-squark mass eigenstate t˜1 via either t˜2→Ht˜1 or t˜2→Zt˜1, followed in both cases by t˜1→tχ˜10, where χ˜10 is an undetected, stable, lightest supersymmetric particle. The interpretation is performed in the region where the mass difference between the t˜1 and χ˜10 states is approximately equal to the top-quark mass (mt˜1−mχ˜10≃mt), which is not probed by searches for direct t˜1 squark pair production. The analysis excludes top squarks with masses mt˜2<575GeV and mt˜1<400GeV at a 95% confidence level.