The production of a Higgs boson with central rapidity, decaying to bb and accompanied by two jets that are forward in rapidity is presented as an important class of events at the Large Hadron Collider. Specifically, we study central Z boson production accompanied by rapidity gaps on either side as a way to gauge Higgs production via weak boson fusion at the LHC. We analyse the possible backgrounds for the bb decay mode and show that these can be substantially reduced. Special attention is paid to the evaluation of the gap survival factor, which is the major source of theoretical uncertainty in the rate of H, Z and W central production events with rapidity gaps. More generally, in relation to Higgs plus forward jet production, we consider the hadronic radiation patterns for the generic process of bb plus two forward jet production at the LHC, where the (centrally produced) bb originate either from a Higgs, a Z or from standard QCD production processes. A numerical technique for evaluating the radiation patterns for non-trivial final states is introduced and shown to agree with the standard analytic results for more simple processes. Significant differences between the radiation patterns for the Higgs signal and the background processes are observed and quantified. This suggests that hadronic radiation patterns could be used as an additional diagnostic tool in Higgs searches in this channel at the LHC. We also study the applicability of an equivalent photon/gluon approximation in describing events with a central system accompanied by two forward jets.