Differential studies of the proton-helium scattering problem using the two-center wave-packet convergent close-coupling approach is extended to the calculation of the ionization cross section differential in the electron emission energy and the projectile scattering angle. The results obtained using the correlated two-electron and effective one-electron methods are in reasonably good agreement with experiment. While the shape of the doubly differential cross section generally agrees with the results of the experiment, at some emission energies its magnitude does not. This appears consistent with similar disagreement seen in the singly differential cross section at the same emission energies.