Four Cu(II)-based neutral coordination polymers, 1D {[Cu(isonia)₂(adi)(dmf)].0.5H₂adi}_n (1), 2D {[Cu(isonia)₂(adi)](H₂O.H₂adi)}_n (2), 1D {[Cu(pic)(CH₃COO)(bpe)].H₂O}_n (3), and 2D [Cu₂(pic)₂(CH₃COO)₂(bpy)]_n (4) with biocompatible molecules: isonicotinamide (isonia), pyridine-2-carboxylic (picolinic, Hpic) and adipic (H₂adi) acids and 1,2-bis(4-pyridyl)-ethane (bpe) and 4,4′-bipyridine (bpy) as neutral linkers are reported. The polymer extension in 1 and 2 is reached via bidentate bridging adi anions with isonia ligands as single (1) and double (2) pillars. 1D and 2D coordination arrays are associated in elegant 3D H-bonded networks via interplay of robust amide(isonia)^…amide(isonia) homosynthon and NH^…O(COO^–) side interactions. In 3 the pic residue coordinates in a chelate mode and forms the five-membered [Cu(pic)] corner fragment. The structure expansion occurs via bidentate-bridging bpe neutral linker registered in a coordination wire as different conformers thus providing long (Cu-bpe)₆ crystallographically unique chain fragment. Oppositely, in 4 the pic residue acts in a bidentate chelate bridging mode and gives rise to the 2D coordination array. The bpy trapping between each two Cu(II) atoms, does not participate in further structure extension. The decisive impact of amido-group of isonia ligand in structure rigidification and retention of protic H₂adi and water guest molecules is demonstrated. The gradual decrease of guest's capacity correlates with an increased liphophilicity of 3 and 4 comparing with 1 and 2.