We have investigated coupled layers of electron and hole liquids in semiconductor heterostructures in zero magnetic field for densities ${\mathit{r}}_{\mathit{s}}$\ensuremath{\lesssim}20 using the Singwi-Tosi-Land-Sj\"olander self-consistent formalism generalized for layers of unequal density. We calculate susceptibilities, local fields, pair correlation functions, and the dispersion of the collective modes for a range of layer spacings. We include cases where the densities in the two layers are not equal. We find generally that static correlations acting between layers do not have a large effect on the correlations within the layers. For coupled electron-hole layers we find that as the spacing between the layers decreases there is a divergence in the static susceptibility of the liquid that signals an instability towards a charge-density-wave ground state. When the layer spacing approaches the effective Bohr radius the electron-hole correlation function starts to diverge at small interparticle separations. This effect is a precursor to the onset of excitonic bound states but this is preempted by the charge-density-wave instability. The acoustic plasmon exhibits a crossover in behavior from a coupled mode to a mode that is confined to a single layer. Correlations sometimes push the acoustic plasmon dispersion curve completely into the single-particle excitation spectrum. For layers with different densities the Landau damping within the single-particle excitation region is sometimes so weak that the acoustic plasmon can exist inside the region as a sharp resonance. We find for the electron-hole case that proximity to the charge-density-wave instability has an unusual effect on the dispersion of the optical plasmon mode. \textcopyright{} 1996 The American Physical Society.