[en] Angular distributions of charged dissociation fragments are measured for 3.0-MeV H₂⁺ and 3.63-MeV HeH⁺ ions incident on approx. 160 A carbon targets. By using the reflection method for a pure Coulomb potential, there are unfolded from these data the distributions of internuclear separations for each molecular-ion species prior to dissociation. These results are insensitive to ion-source conditions. For H₂⁺ this distribution, while approx. 2 times wider than a pure ground vibrational state population, is markedly different from the Franck-Condon distribution that has been previously assumed by other authors with similar rf and duo-plasmatron ion sources. For HeH⁺ the distribution is slightly broader (approx. 1.5 times) than that expected for a pure ground state population. From the data, the initial vibrational state population in the incident beam can be extracted. 11 references