We consider the Higgsstrahlung process in hadronic collisions and present the computation of next-to-next-to-leading order predictions matched to parton showers for both production and H → boverline{b} decay employing the MiNNLOPS method. We present predictions for ZH and W±H production including spin correlations and off-shell effects by calculating the full processes pp → ℓ+ℓ−H → ℓ+ℓ− boverline{b} , pp → {nu}_{ell }{overline{nu}}_{ell }H → {nu}_{ell }{overline{nu}}_{ell }boverline{b} and pp → ℓ±νℓH → {ell}^{pm }{overline{nu}}_{ell }boverline{b} in the narrow-width approximation for the Higgs boson. For the W±H process, NNLO+PS accuracy in production and decay is achieved for the first time. Our calculations are validated against earlier simulations in the NNLOPS approach that includes NNLO corrections via multi-differential reweighting. The new MiNNLOPS generators for these processes, which evaluate NNLO corrections on-the-fly in the event generation, will supersede those earlier calculations. Our predictions are in good agreement with recent measurements of the Higgsstrahlung cross sections.