Charge transport in an electron-hole plasma driven by high-field terahertz (THz) pulses is strongly influenced by electron-hole interactions, as has been shown in a recent publication [P. Bowlan et al., Phys. Rev. Lett. 107, 256602 (2011)]. We introduce a picture of high-field THz transport which accounts for the roles of both types of carriers including their interactions. While holes make a negligible contribution to the current, they are heated by absorbing energy from the driving THz field and introduce a friction force for the electrons over a period of about 500 fs. Our model uses an extended version of the loss-function concept to calculate the time-dependent friction. The local field that drives the electrons differs from the incident THz field by screening due to Coulomb correlations in the plasma. We illustrate how spatial correlations between charged particles (electrons, holes, impurities) create a significant local-field correction to the THz driving field. The dominant contribution stems from Coulomb-correlated heavy-hole wave packets, which are strongly polarizable via inter-valence-band transitions.