The electron density distribution of the ferrimagnetic MnCu(pba)(H2O)3.2H2O chain compound, where pba stands for 1,3-propylenebis(oxamato), has been derived from high resolution X-ray diffraction measurements at 114 K using a multipolar model. The analysis of the chemical bonding has been carried out through the "Atoms in Molecules" formalism and thoroughly interpreted with regards to the strong intrachain and weak interchain magnetic couplings. The topological properties of the electron density on the oxamato bridge indicate large electron delocalization and conjugation effects, in addition to high charge transfer from both metals to the bridge. The resulting positive charges on Mn (+1.45 e) and Cu (+1.56 e) induce charge polarization of the bridge, leading to a shift of electron density from the central C atoms to the metal coordinating O and N atoms. The Mn-bridge interactions are mainly closed-shell interactions with low electron density at the corresponding bond critical points, whereas the Cu-bridge interactions exhibit significant covalent character. The Cu-N bonds are moreover stronger than the Cu-O bonds. The 3d Cu and Mn orbital populations are consistent with pyramidal and regular octahedral environments, respectively, in agreement with the loss of degeneracy due to ligand field effects. Interchain interaction pathways are evidenced by the existence of four bond critical points in hydrogen bond regions. Finally, these intrachain and interchain bonding features are correlated to the results of experimental and theoretical spin density distributions, as well as magnetic measurements.