The five metal azolate/carboxylate (MAC) compounds [Cd(dmpzc)(DMF)(H2O)] (Cd-dmpzc), [Pd(H2dmpzc)2Cl2] (Pd-dmpzc), [Cu(Hdmpzc)2] (Cu-dmpzc), [Zn4O(dmpzc)3]·Solv (Zn-dmpzc·S), and [Co4O(dmpzc)3]·Solv (Co-dmpzc·S) were isolated by coupling 3,5-dimethyl-1H-pyrazol-4-carboxylic acid (H2dmpzc) to cadmium(II), palladium(II), copper(II), zinc(II), and cobalt(II) salts. While Cd-dmpzc and Pd-dmpzc had never been prepared in the past, for Cu-dmpzc, Zn-dmpzc·S, and Co-dmpzc·S we optimized alternative synthetic paths that, in the case of the copper(II) and cobalt(II) derivatives, are faster and grant higher yields than the previously reported ones. The crystal structure details were determined ab initio (Cd-dmpzc and Pd-dmpzc) or refined (Cu-dmpzc, Zn-dmpzc·S, and Co-dmpzc·S) by means of powder X-ray diffraction (PXRD). While Cd-dmpzc is a nonporous 3D MAC framework, Pd-dmpzc shows a 3D hybrid coordination/hydrogen-bonded network, in which Pd(H2dmpzc)2Cl2 monomers are present. The thermal behavior of the five MAC compounds was investigated by coupling thermal analysis to variable-temperature PXRD. Their catalytic activity was assessed in oxidative and C-C coupling reactions, with the copper(II) and cadmium(II) derivatives being the first nonporous MAC frameworks to be tested as catalysts. Cu-dmpzc is the most active catalyst in the partial oxidation of cyclohexane by tert-butyl hydroperoxide in acetonitrile (yields up to 12% after 9 h) and is remarkably active in the solvent-free microwave-assisted oxidation of 1-phenylethanol to acetophenone (yields up to 99% at 120 °C in only 0.5 h). On the other hand, activated Zn-dmpzc·S (Zn-dmpzc) is the most active catalyst in the Henry C-C coupling reaction of aromatic aldehydes with nitroethane, showing appreciable diastereoselectivity toward the syn-nitroalkanol isomer (syn:anti selectivity up to 79:21).