New porous metal-organic frameworks (MOF) [Cd7(Btdc)7(Bpa)2(Dmf)2(H2O)2] · 15Dmf · 2H2O (I) and [Cd7(Btdc)7(Bpe)2(Dmf)2] · 15Dmf · 3H2O (II) (H2Btdc is 2,2’-bithiophene-5,5’-dicarboxylic acid, Bpa is 1,2-bis(4-pyridyl)ethane, Bpe is 1,2-bis(4-pyridyl)ethylene, and Dmf is N,N-dimethylformamide) are synthesized under solvatothermal conditions. The structures and compositions of the compounds are determined by single-crystal X-ray diffraction (XRD) (CIF files ССDС nos. 2364290 (I) and 2364289 (II)) and confirmed by powder XRD, elemental analysis, thermogravimetry, and IR spectroscopy. Compound I has a 2D structure based on the heptanuclear discrete building unit {Cd7} with the linear structure. Compound II is a 3D MOF in which the {Cd7} building units are linked into a continuous chain motif due to additional interactions. The formation of discrete or continuous chains is directly related to the nature of the N-donor bridging ligand (Bpe or Bpa). Compounds I and II have open structures with the accessible volume about 50%. The solvate molecules are replaced by thiophene, benzene, and pyridine, and the luminescence properties of the prepared adducts are studied. Luminescence quenching in the presence of thiophene and an increase in the luminescence intensity in the presence of pyridine accompanied by a change in the quantum yield by 4–5 times are shown.