We calculate the thermally averaged probability distribution for the out-of-plane inversion motion of the CH3+ and H3O+ molecules. Such distributions can be obtained experimentally by using Coulomb explosion imaging (CEI) techniques, and our results will be useful in the interpretation of such images. We calculate these probability distributions from the molecular wavefunctions that we obtain by solving variationally the nine-dimensional rotation–vibration Schrödinger equation using the recently developed ‘XY3’ Hamiltonian and computer program.