A bstract A search is conducted for new resonances decaying into a W or Z boson and a 125 GeV Higgs boson in the $$ \nu \overline{\nu}b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ν</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , $$ {\ell}^{\pm}\nu b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>±</mml:mo> </mml:msup> <mml:mi>ν</mml:mi> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , and $$ {\ell}^{+}{\ell}^{-}b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> final states, where ℓ ± = e ± or μ ± , in pp collisions at $$ \sqrt{s}=13 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> </mml:math> TeV. The data used correspond to a total integrated luminosity of 36.1 fb −1 collected with the ATLAS detector at the Large Hadron Collider during the 2015 and 2016 data-taking periods. The search is conducted by examining the reconstructed invariant or transverse mass distributions of W h and Zh candidates for evidence of a localised excess in the mass range of 220 GeV up to 5 TeV. No significant excess is observed and the results are interpreted in terms of constraints on the production cross-section times branching fraction of heavy W ′ and Z ′ resonances in heavy-vector-triplet models and the CP-odd scalar boson A in two-Higgs-doublet models. Upper limits are placed at the 95% confidence level and range between 9 . 0 × 10 −4 pb and 7 . 3 × 10 −1 pb depending on the model and mass of the resonance.