The radical cation salt, ET2MnCuN(CN)(2), [ET=bis(ethylenedithio)tetrathiafulvalene] with an unusual three-dimensional anionic polymeric network is studied by x-ray diffraction, static susceptibility measurements, and electron spin resonance (ESR) at frequencies between 9 and 420 GHz. The magnetic properties are determined by the alternating two-dimensional layers of the Mn2+ ions of the network and the partially charged ET molecules. At ambient temperature the overlap between Mn2+ ions and ET molecules is weak and an exchange integral vertical bar J(Mn-ET)vertical bar approximate to 4.10(-2) K is estimated from their resolved ESR lines. At lower temperatures, ET2MnCuN(CN)(2) is not a simple system of weakly interacting paramagnetic ions in spite of the isotropic, Curie-like static susceptibility. There are first-order phase transitions at 292 K and in the range of 120-180 K. One of the lattice constants shows anomalous temperature dependence below 292 K. Anisotropic ESR shifts appear below 150 K, which we explain by demagnetizing fields of the platelike crystals and an exchange-narrowed fine structure. The latter contributes significantly to the shift when the populations of Zeeman levels are altered in high magnetic fields at low temperatures. We estimated the exchange coupling between Mn2+ ions within a layer, J(Mn-Mn)approximate to-48 K and determined the fine structure parameters below 150 K, showing a distortion in the plane of the Mn2+ ions.