We report the syntheses, crystal structures, and magnetic properties of KMn(2)(H(3)O(2))(MoO(4))(2) (MnH), KMn(2)(D(3)O(2))(MoO(4))(2) (MnD), KFe(2)(H(3)O(2))(MoO(4))(2) (FeH), KFe(2)(D(3)O(2))(MoO(4))(2) (FeD), KCo(2)(H(3)O(2))(MoO(4))(2) (CoH), and KCo(2)(D(3)O(2))(MoO(4))(2) (CoD), and the magnetic structures of MnD and FeD. They belong to the structural variant (space group I2/m) of the mineral natrochalcite NaCu(2)(H(3)O(2))(SO(4))(2) (space group C2/m) where the diagonal within the ac-plane of the latter become one axis of the former. The structure of MnD, obtained from Rietveld refinement of a high-resolution neutron pattern taken at 300 K, consists of chains of edge-sharing octahedra bridged by MoO(4) and D(3)O(2) to form layers, which are connected to K through the oxygen atoms to form the three-dimensional (3D)-network. The X-ray powder diffraction patterns of the other two compounds were found to belong to the same space group with similar parameters. The magnetic susceptibilities of MnH and FeH exhibit long-range ordering of the moments at a Néel temperature of 8 and 11 K, respectively, which are accompanied by additional strong Bragg reflections in the neutron diffraction in the ordered state, consistent with antiferromagnetism. Analyses of the neutron data for MnD and FeD reveal the presence of both long- and short-range orderings and commensurate magnetic structures with a propagation vector of (½, 0, ½). The moments are antiferromagnetically ordered within the chains with alternation between chains to generate four nonequivalent nuclear unit cells. For MnD the moments are perpendicular to the chain axis (b-axis) while for FeD they are parallel to the b-axis. The overall total is a fully compensated magnetic structure with zero moment in each case. Surprisingly, for KCo(2)(D(3)O(2))(MoO(4))(2) neither additional peaks nor increase of the nuclear peaks' intensities were observed in the neutron diffraction patterns below the magnetic anomaly at 12 K which was identified to originate from a small quantity of a ferromagnetic compound, Co(2)(OH)(2)MoO(4).