We report variational and diffusion quantum Monte Carlo calculations of the binding energies of indirect trions and biexcitons in ideal two-dimensional bilayer systems within the effective-mass approximation, and with a Coulomb 1/r interaction between charge carriers. The critical layer separation at which trions become unbound has been studied for various electron-hole mass ratios, and found to be over an order of magnitude larger than the critical layer separation for biexcitons.