  We propose differential observables for $pp \to Z(\ell^+\ell^-)h(b\bar{b})$
that can be used to completely determine the tensor structure of the
$hZZ^*/hZ\bar{f}f$ couplings relevant to this process in the dimension-6 SMEFT.
In particular, we propose a strategy to probe the anomalous $h Z_{\mu
\nu}Z^{\mu \nu}$ and $h Z_{\mu \nu}\tilde{Z}^{\mu \nu}$ vertices at the percent
level. We show that this can be achieved by resurrecting the interference term
between the transverse $Zh$ amplitude, which receives contributions from the
above couplings, and the dominant SM longitudinal amplitude. These
contributions are hard to isolate without a knowledge of the analytical
amplitude, as they vanish unless the process is studied differentially in three
different angular variables at the level of the $Z$-decay products. By also
including the differential distributions with respect to energy variables, we
obtain projected bounds for the two other tensor structures of the Higgs
coupling to $Z$-bosons.
