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 ET>~15GeV and pseudorapidity |η|<~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 a transverse momentum larger than 8GeV/c. Jets containing hadrons with heavy flavor are selected via the identification of secondary vertices. The parton-level cross sections predicted by the 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 bb¯ 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 (pT>~2GeV/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.