  We study $4b+2\tau$ and $4b+1\tau$ signatures of heavy neutral and charged
Higgs bosons originating from cascade decays of pair-produced new quarks.
Decays of vectorlike quarks through heavy Higgses can easily dominate in the
two Higgs doublet model of type-II, and the studied signatures are common to
many possible decay chains. We design search strategies for these final states
and discuss the mass ranges of heavy Higgs bosons and new quarks that can be
explored at the Large Hadron Collider as functions of branching ratios in a
model independent way. We further combine the results with a similar study
focusing on decays which lead to a $6b$ final state and interpret the
sensitivity to charged and neutral Higgs bosons and vectorlike quarks in the
type-II two Higgs doublet model. We find that the LHC reach for their masses
extends to well above 2 TeV in the case of an SU(2) doublet quark and to at
least 1.8 TeV for a bottom-like SU(2) singlet quark in the whole range of
$\tan\beta$ between 1 and 50.
