We present a four-body model for double charge transfer, called the four-body double-capture model. This model explicitly treats all four particles in the collision, and we apply it here to fully differential cross sections (FDCSs) for proton+helium collisions. The effects of initial- and final-state electron correlations are studied, as well as the role of the projectile-nucleus interaction. We also present results for proton+helium single capture, as well as single-capture:double-capture ratios of FDCSs.