The quantum electrostatic heterostructure (QEH) model allows for efficient computation of the dielectric screening properties of layered van der Waals (vdW)-bonded heterostructures in terms of the dielectric functions of the individual two-dimensional (2D) layers. Here, we extend the QEH model by including (1) contributions to the dielectric function from infrared active phonons in the 2D layers, (2) screening from homogeneous bulk substrates, and (3) intraband screening from free carriers in doped 2D semiconductor layers. We demonstrate the potential of the extended QEH model by calculating the dispersion of coupled phonons in multilayer stacks of hexagonal boron-nitride (hBN), the strong hybridization of plasmons and optical phonons in graphene/hBN heterostructures, the effect of substrate screening on the exciton series of monolayer MoS2, and the properties of hyperbolic plasmons in a doped phosphorene sheet. The new QEH code is distributed as a Python package with a simple command line interface and a comprehensive library of dielectric building blocks for the most common 2D materials, providing an efficient open platform for dielectric modeling of realistic vdW heterostructures.