  We consider the simultaneous measurement of the Higgs
($p_t^{\tiny{\mbox{H}}}$) and the leading jet ($p_t^{\tiny{\mbox{J}}}$)
transverse momentum in hadronic Higgs-boson production, and perform the
resummation of the large logarithmic corrections that originate in the limit
$p_t^{\tiny{\mbox{H}}}\,,p_t^{\tiny{\mbox{J}}} \ll m_{\tiny{\mbox{H}}}$ up to
next-to-next-to-leading-logarithmic order. This work constitutes the first
simultaneous (double differential) resummation for two kinematic observables of
which one involves a jet algorithm in hadronic collisions, and provides an
important milestone in the theoretical understanding of joint resummations. As
an application, we provide precise predictions for the Higgs
transverse-momentum distribution with a veto $p_t^{\tiny{\mbox{J}}} \leq
p_{t}^{\tiny{\mbox{J,v}}}$ on the accompanying jets, whose accurate description
is relevant to the Higgs precision programme at the Large Hadron Collider.
