  We investigate the effects of an all order QCD resummation of soft gluon
emissions for Higgs boson production in association with two hard jets. We
consider both the gluon-gluon fusion and weak boson fusion processes and show
how to resum a large part of the leading logarithms in the jet veto scale. Our
resummation improves on previous analyses which also aim to include the effects
of multiple soft gluon radiation. In addition we calculate the interference
between weak boson fusion and gluon-gluon fusion and find that it is small.
