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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 theresummation 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 tonext-to-next-to-leading-logarithmic order. This work constitutes the firstsimultaneous (double differential) resummation for two kinematic observables ofwhich one involves a jet algorithm in hadronic collisions, and provides animportant milestone in the theoretical understanding of joint resummations. Asan application, we provide precise predictions for the Higgstransverse-momentum distribution with a veto $p_t^{\tiny{\mbox{J}}} \leqp_{t}^{\tiny{\mbox{J,v}}}$ on the accompanying jets, whose accurate descriptionis relevant to the Higgs precision programme at the Large Hadron Collider.

Higgs transverse momentum with a jet veto: a double-differential resummation