We investigate the chemical and kinematic properties of the diffuse stellar haloes of six simulated Milky-Way-like galaxies from the Aquarius Project. Binding energy criteria are adopted to define two dynamically distinct stellar populations: the diffuse inner and outer haloes, which comprise different stellar subpopulations with particular chemical and kinematic characteristics. Our simulated inner- and outer-halo stellar populations have received contributions from debris stars (formed in subgalactic systems while they were outside the virial radius of the main progenitor galaxies) and endo-debris stars (those formed in gas-rich subgalactic systems inside the dark matter haloes of the main progenitor galaxy). The inner haloes possess an additional contribution from disc-heated stars, in the range ∼3–30 per cent, with a mean of ∼20 per cent. Disc-heated stars might exhibit signatures of kinematical support, in particular among the youngest ones. Endo-debris plus disc-heated stars define the so-called in situ stellar populations. In both the inner- and outer-halo stellar populations, we detect contributions from stars with moderate to low [α/Fe] ratios, mainly associated with the endo-debris or disc-heated subpopulations. The observed abundance gradients in the inner-halo regions are influenced by both the level of chemical enrichment and the relative contributions from each stellar subpopulation. Steeper abundance gradients in the inner-halo regions are related to contributions from the disc-heated and endo-debris stars, which tend to be found at lower binding energies than debris stars. In the case of the outer-halo regions, although [Fe/H] gradients are relatively mild, the steeper profiles arise primarily due to contributions from stars formed in more massive satellites, which sink farther into the main halo system, and tend to have higher levels of chemical enrichment and lower energies. Our findings support the existence of (at least) two distinct diffuse stellar halo populations, as suggested by a number of recent observations in the Milky Way and M31. Our results also indicate that a comparison of the range of predicted kinematics, abundance gradients and frequency of [α/Fe]-deficient stars with observations of these quantities in the Milky Way, M31 and other large spirals can both provide clues to improve the modelling of baryonic physics, and reveal detailed information about their likely history of formation and evolution.