  We study a set of exclusive decay modes of the Standard Model Higgs boson
into a vector meson and a dilepton pair: $h\to V \ell^+ \ell^-$, with
$V=\Upsilon, J/\psi,\phi$, and $\ell=\mu, \tau$, determining the decay rates,
the dilepton mass spectra and the $V$ longitudinal helicity fraction
distributions. In the same framework, we analyze the exclusive modes into
neutrino pairs $h\to V \nu \bar \nu$. We also discuss the implications of the
recent CMS and ATLAS results for the lepton flavor-changing process $h\to
\tau^+ \mu^-$ on the $h\to V \tau^+ \mu^-$ decay modes.
