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 → $$ b\overline{b} $$
b
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−$$ b\overline{b} $$
b
b
¯
, pp → $$ {\nu}_{\ell }{\overline{\nu}}_{\ell }H $$
ν
ℓ
ν
¯
ℓ
H
→ $$ {\nu}_{\ell }{\overline{\nu}}_{\ell }b\overline{b} $$
ν
ℓ
ν
¯
ℓ
b
b
¯
and pp → ℓ±νℓH → $$ {\ell}^{\pm }{\overline{\nu}}_{\ell }b\overline{b} $$
ℓ
±
ν
¯
ℓ
b
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.