Atomic systems placed in external potentials manifest various characteristic features which provide useful knowledge about the surroundings. We have studied the structural properties of the ground state of different two-electron systems under isotropic harmonic confinement (IHC). In particular, we have considered negative hydrogen ion, neutral helium atom and positive singly ionized lithium ion to cover all types of charge states. In addition, we have also studied the system of two electrons inside IHC. The wave function is expanded in Hylleraas basis to incorporate the effect of electron correlation in an explicit manner and Ritz variational calculations are performed to obtain the energy eigenvalues and the relative wave functions. The energy levels become more positive with increasing strength of the confining potential. The results show that for ionic systems, the two-electron energy level crosses the respective one-electron threshold at a certain value of the potential beyond which the two-electron level becomes quasi-bound. In order to get deeper insight into such threshold ionization phenomenon, we have examined the contribution of the correlated energy E_ corr E corr sum of radial and angular correlation energy and radial correlation energy E_ rad. corr E rad. corr to the total energy for different two-electron systems under IHC. The Hellmann–Feynman theorem and the virial theorem have been verified as a quantitative validation of the accuracy of our results. The one-and two-electron radial densities have also been analyzed to gain a physical insight into the structural changes of the two-electron systems under IHC. Moreover, the expectation values of different radial and angular variables are also reported which are important to estimate different geometrical and spectral properties. Graphic abstract