The compounds BaDy₂O₄ and BaHO₂O₄ are part of a family of frustrated systems exhibiting interesting properties, including spin-liquid-type ground states, magnetic-field-induced phases, and the coexistence of short- and long-range magnetic order, with dominant one-dimensional correlations, which can be described as Ising J₁-J₂ zigzag chains along the c axis. We have investigated polycrystalline samples of BaDy₂O₄ and BaHO₂O₄ with both neutron diffraction and neutron spectroscopy, coupled to detailed crystalline electric field calculations. The latter points to site-dependent anisotropic magnetism in both materials, which is corroborated by the magnetic structures we determined. The two systems show the coexistence of two different long-range orders: two double Néel ↑↑↓↓ orders in the ab plane with propagation vectors k₁=(½, 0, ½) and k₂=(½, ½, ½) for BaDy₂O₄, and two distinct arrangements of simple Néel ↑↓↑↓ orders along the c axis, both with the propagation vector k₀=(0, 0, 0) for BaHO₂O₄. The order for both wave vectors in BaDy₂O₄ occurs at T_N=0.48 K, while in BaHO₂O₄ the first order sets in at T_N ∼ 1.3 K and the second one has a lower ordering temperature of 0.84 K. Both compounds show extensive diffuse scattering which we successfully modeled with a one-dimensional axial next-nearest neighbor Ising (ANNNI) model. In both materials, strong diffusive scattering persists to temperatures well below where the magnetic order is fully saturated.