The reaction of the bis(1,2-ditiolene) complex [Pd(Me₂timdt)₂] (1; Me₂timdt^•– = monoreduced 1,3-dimethyl-2,4,5-trithioxoimidazolidine) with Br₂ yielded the complex [Pd(Me₂timdt)Br₂] (2), which was reacted with Na₂mnt (mnt^2– = 1,2-dicyano-1,2-ethylenedithiolate) to give the neutral mixed-ligand complex [Pd(Me₂timdt)(mnt)] (3). Complex 3 shows an intense solvatochromic near-infrared (NIR) absorption band falling between 955 nm in DMF and 1060 nm in CHCl₃ (ε = 10700 M^–1 cm^–1 in CHCl₃). DFT calculations were used to elucidate the electronic structure of complex 3, and to compare it with those of the corresponding homoleptic complexes 1 and [Pd(mnt)₂] (4). An in-depth comparison of calculated and experimental structural and vis–NIR spectroscopic properties, supported by IEF-PCM TDDFT and NBO calculations, clearly points to a description of 3 as a dithione-dithiolato complex. For the first time, a Broken-Symmetry (BS) procedure for the evaluation of the singlet diradical character (DC) of heteroleptic bis(1,2-dithiolene) complexes has been developed and applied to complex 3. The DC, predominant for 1 (n_DC = 55.4%), provides a remarkable contribution to the electronic structures of the ground states of both 3 and 4, showing a diradicaloid nature (n_DC = 24.9% and 27.5%, respectively). The computational approach developed here clearly shows that a rational design of the DC of bis(1,2-ditiolene) metal complexes, and hence their linear and nonlinear optical properties, can be achieved by a proper choice of the 1,2-dithiolene ligands based on their electronic structure.