We report synthesis and composite study of a novel metal–organic framework (MOF) compound of chemical formula _∞³[Cu₂^ICu₂^II{H₂O}₂{(Me–trz–mba)₂thio}₂]Cl₂, where (Me–trz–mba)₂thio^2– stands for 3,3-(5,5-(thiophene-2,5-diyl)bis(3-methyl-4H-1,2,4-triazole-5,4-diyl))dibenzoate. This coordination polymer was synthesized by solvothermal synthesis. The crystal structure was determined using single crystal X-ray diffraction. The main building block of this compound is a so-called Cu₂ paddle-wheel (PW) unit, which contains two Cu²⁺ ions connected via four carboxylate groups. Magnetic properties of the investigated MOF were studied by continuous-wave electron paramagnetic resonance (EPR) spectroscopy at X- and Q-band frequencies in a wide temperature range. Mononuclear Cu²⁺ ions were observed in the EPR spectra and characterized by spectral simulations. In addition, the obtained EPR data allowed us to detect and investigate three distinct magnetic interactions related to the Cu²⁺ pairs. At higher temperatures the fine structure pattern was observed in the EPR spectra and the spin–spin interaction tensor D was determined. The origin of this pattern was assigned to the thermally populated excited triplet states of the Cu²⁺ pairs. It was found that two Cu²⁺ ions within a single PW unit couple antiferromagnetically with the exchange coupling constant J = −258 cm^–1. Moreover, the EPR spectra of dehydrated MOF samples show a broad, poorly resolved spectral feature, the origin of which is an exchange of the spin triplets between neighboring Cu₂ PW units. By simulating the powder pattern of this interdinuclear exchange line, we estimated the exchange coupling between neighboring PW units (|J′| = 4.9 cm^–1). It was also found that the interdinuclear exchange gradually disappears, if the dehydrated samples are allowed to interact with air, demonstrating that this exchange can be rather easily manipulated in the investigated MOF.