  We present a detailed examination of the heavy flavor properties of jets
produced at the Fermilab Tevatron collider. The data set, collected with the
Collider Detector at Fermilab, consists of events with two or more jets with
transverse energy $E_T \geq 15$ GeV and pseudo-rapidity $|\eta| \leq 1.5$. The
heavy flavor content of the data set is enriched by requiring that at least one
of the jets (lepton-jet) contains a lepton with transverse momentum larger than
8 GeV/c. Jets containing hadrons with heavy flavor are selected via the
identification of secondary vertices.
  The parton-level cross sections predicted by the {\sc herwig} Monte Carlo
generator program are tuned within theoretical and experimental uncertainties
to reproduce the secondary-vertex rates in the data.
  The tuned simulation provides new information on the origin of the
discrepancy between the $b\bar{b}$ cross section measurements at the Tevatron
and the next-to-leading order QCD prediction. We also compare the rate of
away-jets (jets recoiling against the lepton-jet) containing a soft lepton
($p_T \geq 2$ GeV/c) in the data to that in the tuned simulation.
  We find that this rate is larger than what is expected for the conventional
production and semileptonic decay of pairs of hadrons with heavy flavor.
