In addition to being a solution to the little hierarchy problem, the Mirror Twin Higgs provides a natural setting for Asymmetric Dark Matter. In its incarnation with only one Higgs doublet and its mirror copy, dark matter would however almost certainly consist mostly of mirror atoms, which is severely ruled out by constraints on dark matter self-interactions. By adding a second Higgs doublet and its mirror, the vevs of the different Higgses can be arranged such that dark matter consists mostly of mirror neutrons, which is cosmologically viable. In this paper, it is shown that current constraints from colliders, flavour and cosmology can accommodate such a vev structure with little increase in the necessary tuning.