Double-electron capture by the impact of heavy projectiles on heliumlike atoms is studied with a two-electron model. The process is here considered a two-step collision, which in the frame of the distorted-wave formalism is related to the second order. This second order is evaluated by using an on-shell Green function representing one electron in each center, and it is found to be related, after some approximations, to the independent-electron model. In particular, the exact impulse approximation is used to calculate the single-capture T-matrix elements, and the electronic repulsion is included as a dynamic perturbation in first order. A configuration-interaction wave function is employed to describe the ground state of helium for double capture 1 s 2→ 1 s 2 in a He 2+-He collision. For this benchmark, differences with the use of a Hartree-Fock wave function instead are found to be negligible. Thereafter, capture to single excited states for the same system is calculated by using Hartree-Fock and variational electronic wave functions. Also, double capture for multiply charged ions on helium is calculated. Differential cross sections for double-capture He 2+-He collisions at 60 keV/amu impact energy are presented and compared with previous experiments. The present theory produces good agreement with the available data.