This article presents a search for new resonances decaying into a Z or W boson and a 125 GeV Higgs boson h , and it targets the $$ \nu \overline{\nu}b\overline{b} $$ ν ν ¯ b b ¯ , $$ {\ell}^{+}{\ell}^{-}b\overline{b} $$ ℓ + ℓ − b b ¯ , or $$ {\ell}^{\pm}\nu b\overline{b} $$ ℓ ± νb b ¯ final states, where ℓ = e or μ , in proton-proton collisions at $$ \sqrt{s} $$ s = 13 TeV. The data used correspond to a total integrated luminosity of 139 fb ^{− 1} collected by the ATLAS detector during Run 2 of the LHC at CERN. The search is conducted by examining the reconstructed invariant or transverse mass distributions of Zh or Wh candidates for evidence of a localised excess in the mass range from 220 GeV to 5 TeV. No significant excess is observed and 95% confidence-level upper limits between 1.3 pb and 0.3 fb are placed on the production cross section times branching fraction of neutral and charged spin-1 resonances and CP-odd scalar bosons. These limits are converted into constraints on the parameter space of the Heavy Vector Triplet model and the two-Higgs-doublet model.