We perform a comprehensive study of the effects related to a heavy-quark threshold in the production and decay of a scalar or pseudoscalar Higgs particle. We study the QCD corrections to the decay mode into a quark-antiquark pair and also the mixing of a Higgs boson with quarkonium states, both below and above the open-flavor threshold, which can change the properties of the Higgs boson drastically. Numerical results for a Higgs boson of mass around 10 GeV, where the mixing with bb» states has a great influence on the decay widths and branching ratios, are worked out in detail for the cases of the standard model and minimal supersymmetry. The production cross section of a Higgs particle can also be enhanced by mixing with a quarkonium. A possibility to search for a Higgs boson in the 10-GeV mass range via +- decays in fixed-target pp experiments at the Fermilab Tevatron or Serpukhov UNK is suggested, and ways to enhance the signal-to-background ratio are discussed.