Two-component quasirelativistic approaches are in principle capable of reproducing results from fully relativistic calculations based on the four-component Dirac equation (with fixed particle number). For one-electron systems, this also holds in practice, but in many-electron systems one has to transform the two-electron interaction, which is necessary because a picture change occurs when going from the Dirac equation to a two-component method. For one-electron properties, one can take full account of picture change in a manageable way, but for the electron interaction, this would spoil the computational advantages which are the main reason to perform quasirelativistic calculations. Exploiting those picture change effects are largest in the atomic cores, which in molecular applications do not differ too much from the cores of isolated neutral atoms, we propose an elegant, efficient, and accurate approximation to the two-electron picture change problem. The new approach, called the "model potential" approach because it makes use of atomic (four- and two-component) data to estimate picture change effects in molecules, shares with the nuclear-only approach that the Douglas-Kroll operator needs to be constructed only once (not in each self-consistent-field iteration) and that no time-consuming multicenter relativistic two-electron integrals need to be calculated. The new approach correctly describes the screening of both the nearest nucleus and distant nuclei, for the scalar-relativistic as well as the spin-orbit parts of the Hamiltonian. The approach is tested on atomic and molecular-orbital energies as well as spectroscopic constants of the lead dimer.