The layered molybdate [M-2(pzc)(2)(H2O)(x)][Mo5O16] ( I: M = Ni, x = 5.0; II: M = Co, x = 4.0; pzc = pyrazinecarboxylate) hybrid solids were synthesized via hydrothermal reactions at 160 - 165 degrees C. The structures were determined by single-crystal X-ray diffraction data for I (Cc, Z = 4; a = 33.217(4) angstrom, b = 5.6416( 8) angstrom, c = 13.982(2) angstrom, beta = 99.407(8)degrees, and V = 2585.0(6) angstrom(3)) and powder X-ray diffraction data for II (C 2/c, Z = 4; a = 35.42( 6) angstrom, b = 5.697( 9) angstrom, c = 14.28(2) angstrom, beta = 114.95(4 degrees), and V = 2614( 12) angstrom(3)). The polar structure of I contains new [Ni-2(pzc)(2)(H2O)(5)](2+) double layers that form an asymmetric pattern of hydrogen bonds and covalent bonds to stair-stepped [Mo5O16](2-) sheets, inducing a net dipole moment in the latter. In II, however, the [Co-2(pzc)(2)(H2O)(4)](2+) double layers have one less coordinated water and subsequently exhibit a symmetric pattern of covalent and hydrogen bonding to the [Mo5O16](2-) sheets, leading to a centrosymmetric structure. Thermogravimetric analyses and powder X-ray diffraction data reveal that I can be dehydrated and rehydrated with from 0 to 6.5 water molecules per formula unit, which is coupled with a corresponding contraction/expansion of the interlayer distances. Also, the dehydrated form of I can be intercalated by similar to 4.3 H2S molecules per formula unit, but the intercalation by pyridine or methanol is limited to less than one molecule per formula unit.