A new series of cadmium(II) and zinc(II) coordination polymers, formulated as {[Cd1.5(μ-L)(μ-CH3COO)(μ-N3)(CH3OH)]·3CH3OH}n (1), {[Zn(μ-L)Br]·CH3OH}n (2), {[Zn(μ-L)I]·CH3OH}n (3), {[Zn(μ-L)(N3)]·C2H5OH}n (4), and [Zn2(μ-L)2(μ-N3)2]n (5), was self-assembled from the metal(II) acetates (or nitrates), a multifunctional pyridine-hydrazone building block {HL = 2-benzoylpyridine-isonicotinoylhydrazone}, and auxiliary ligands selected from NaN3, KBr, or KI. All products 1–5 were isolated as stable crystalline solids and were fully characterized by elemental analysis, IR spectroscopy, and single-crystal X-ray diffraction. Although in all compounds the pyridine-hydrazone blocks L1− simultaneously act as μ-spacers and N2,O-chelators (adopting the enolic = NNCO form), the structures of 1–5 are modulated by the type of an auxiliary ligand and thus vary from ladder-like double chains in 1 and zigzag 1D chains in 2–4 to intricate 2D layers in 5. Topological analysis of the underlying metal-organic networks revealed the 2C1 (in 2–4) and hcb (in 5) topologies, while a decorated ladder was identified in 1. Besides, the structure of 1 revealed an interesting example of cyclic hexameric (CH3OH)6 clusters formed by H-bonding interactions between adjacent methanol molecules of crystallization. The role of hydrogen bonds, π⋯π interactions, and presence of solvent molecules of crystallization was analyzed from the structural data and by Hirshfeld surface analysis.