The synthesis, structural characterization, topological analysis, proton conductivity, and catalytic properties are reported of two Cu(II)-based compounds, namely a dinuclear Cu(II) complex [Cu2(μ-VPA)2(phen)2(H2O)2]·8H2O (1) (H2VPA = vinylphosphonic acid, phen = 1,10-phenanthroline) and a 1D coordination polymer [Cu(μ-SO4)(phen)(H2O)2]∞ (2). Their structural features and H-bonding interactions were investigated in detail, showing that the metal-organic structures of 1 and 2 are extended by multiple hydrogen bonds to more complex 2D or 1D H-bonded architectures with the kgd [Shubnikov plane net (3.6.3.6)/dual] and SP 1-periodic net (4,4)(0,2) topology, respectively. These nets are primarily driven by the H-bonding interactions involving water ligands and H2O molecules of crystallization; besides, the (H2O)4/(H2O)5 clusters were identified in 1. Both 1 and 2 are moderate proton conductors, with proton conductivity values, σ = 3.65 × 10-6 and 3.94 × 10-6 S·cm-1, respectively (measured at 80 °C and 95% relative humidity). Compounds 1 and 2 are also efficient homogeneous catalysts for the mild oxidative functionalization of C5-C8 cycloalkanes (cyclopentane, cyclohexane, cycloheptane, and cyclooctane), namely for the oxidation by H2O2 to give cyclic alcohols and ketones and the hydrocarboxylation by CO/H2O and S2O82- to the corresponding cycloalkanecarboxylic acids as major products. The catalytic reactions proceed under mild conditions (50-60 °C) in aqueous acetonitrile medium, resulting in up to 34% product yields based on cycloalkane substrate.