  In certain new physics scenarios, a singly charged Higgs boson can couple to
both fermions and $W^\pm Z$ at tree level. We develop new strategies beyond
current experimental searches using $pp\to jjH^\pm$, $H^\pm \to tb $ at the
Large Hadron Collider (LHC). With the effective $H^\pm W^\mp Z$ and $H^\pm tb$
couplings we perform a model-independent analysis at the collision energy
$\sqrt{s}=13$~TeV with the integrated luminosity of $3~\text{ab}^{-1}$. We
derive the discovery prospects and exclusion limits for the charged Higgs boson
in the mass range from 200~GeV to 1~TeV. With $|F_{WZ}|,|A_t|\sim 0.5-1.0$ and
$300~\text{GeV}\lesssim m_{H^\pm}\lesssim 400~\text{GeV}$, we point out that a
discovery significance of $5\sigma$ can be achieved. The constraints and
projected sensitivities are also discussed in a realistic model, i.e., the
modified Georgi-Machacek model without custodial symmetry. Our proposed search
would provide direct evidence for a charged Higgs boson $H^\pm$ that couples to
$W^\pm Z$ and $tb$, which can have better sensitivity to the couplings of
$H^\pm W^\mp Z$ and $H^\pm tb$ than current searches.
