We have modeled the full velocity-resolved reverberation response of the H$beta$ and He II optical broad emission lines in NGC 3783 to constrain the geometry and kinematics of the low-ionization and high-ionization broad line region. The geometry is found to be a thick disk that is nearly face on, inclined at $sim 18^{circ}$ to our line of sight, and exhibiting clear ionization stratification, with an extended H$beta$-emitting region ($r_{rm median}=10.07^{+1.10}_{-1.12}$ light days) and a more compact and centrally-located He II-emitting region ($r_{rm median}=1.33^{+0.34}_{-0.42}$ light days). In the H$beta$-emitting region, the kinematics are dominated by near-circular Keplerian orbits, but with $sim 40$% of the orbits inflowing. The more compact He II-emitting region, on the other hand, appears to be dominated by outflowing orbits. The black hole mass is constrained to be $M_{rm BH}=2.82^{+1.55}_{-0.63}times10^7$ $M_{odot}$, which is consistent with the simple reverberation constraint on the mass based on a mean time delay, line width, and scale factor of $langle f rangle=4.82$. The difference in kinematics between the H$beta$- and He II-emitting regions of the BLR is intriguing given the recent history of large changes in the ionizing luminosity of NGC 3783 and evidence for possible changes in the BLR structure as a result.
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