We present results for $W^\pm Z$ production at NNLO QCD and NLO electroweak (EW) accuracy matched to parton showers. NNLO QCD corrections matched to parton showers are obtained through the $\mathrm{MiNNLO}_\mathrm{PS}$ method, while NLO EW results matched to parton showers are produced using the POWHEG approach. We identify different combination schemes between QCD and EW corrections with QCD and/or QED showers and we conduct a phenomenological study to analyze their capabilities for describing certain kinematic regions of relevant distributions. We present results for the fully leptonic decay channel $pp \to \ell^+\ell^-\ell'^\pm \nu_{\ell'}$, with both $\ell'\neq\ell$ and $\ell'=\ell$, including spin correlation, interferences and off-shell effects. We observe that NNLO QCD corrections with both QCD and QED showers provide an excellent description of the bulk of the cross section, while EW corrections become dominant in the deep tails of kinematic distributions. Our results are in good agreement with recent ATLAS data.