We report EPR measurements in single-crystal samples at the microwave frequencies 9.8 and 34.3 GHz and magnetic susceptibility measurements in polycrystalline samples for the ternary complex of copper with aspartic acid and phenanthroline, (L-aspartato)(1,10-phenanthroline)copper hydrate. The crystal lattice of this compound is composed of two dissimilar copper ions identified as Cu(A) and Cu(B), which are in two types of copper chains called A and B, respectively, running parallel to the b crystal axis. The copper ions in the A chains are connected by the aspartic acid molecule, and those in the B chains by a chemical path that involves a carboxylate bridge and a hydrogen bond, Both chains are held together by a complex network of hydrogen bonds and by hydrophobic interactions between aromatic amines. Magnetic susceptibility data indicate a Curie-Weiss behavior in the studied temperature range (2-300 K). The EPR spectra at 9.8 GHz display a single exchange collapsed resonance for any magnetic field orientation,in the so-called strong exchange regime. Those at 34.3 GHz are within the so-called weak exchange regime and display two resonances which belong to each type of copper ion chain. The decoupling of the spectra at 34.3 GHz using a theory based on Anderson’s model for the case of two weakly exchange coupled spins S = 1/2 allows one to obtain the angular variation of the squares of the g-factor and the peak-to-peak line width of each resonance. This model also allows one to evaluate the exchange parameter J(AB)/k = 2.7(6) mK associated with the chemical path connecting dissimilar copper ions, The line width data obtained for each component of the spectra at 34.3 GHz are analyzed in terms of a model based on Kubo and Tomita’s theory, to obtain the exchange parameters J(A)/k = 0.77(2) K and J(B)/k = 1.44(2) K associated with the chemical paths connecting the similar copper ions of types A and B, respectively.