We investigate interparticle correlations for two layers of charge-carrier liquid trapped in adjacent wells of a gallium arsenide heterostructures. We determine in the absence of appreciable tunneling the static polarizability, the pair correlation functions, and the local-field corrections both within a layer and between the layers. The liquid ground state has points of instability to states that are inhomogeneous in the density. An important result is that, in contrast with electron-electron layers, for electron-hole layers the interlayer correlations favor the formation of the inhomogeneous states. The pair correlation functions display unusual behavior near the points of instability.