  We calculate the order O(alpha^2 alpha_s^3) interference effect between the
gluon fusion and weak boson fusion processes allowed at the one-loop level in
Higgs boson plus 2 jet production at the LHC. The corresponding one-loop
amplitudes, which have not been considered in the literature so far, are
evaluated analytically using dimensional regularisation and the necessary
master integrals with massive propagators are reported. It is discussed in
detail how various mechanisms conspire to make this contribution numerically
negligible for experimental studies at the LHC.
