The mechanochemical synthesis of drug–drug solid forms containing metformin hydrochloride (MET·HCl) and thiazide diuretics hydrochlorothiazide (HTZ) or chlorothiazide (CTZ) is reported. Characterization of these new systems indicates formation of binary eutectic conglomerates, i.e., drug–drug eutectic solids (DDESs). Further analysis by construction of binary diagrams (DSC screening) exhibited the characteristic V-shaped form indicating formation of DDESs in both cases. These new DDESs were further characterized by different techniques, including thermal analysis (DSC), solid state NMR spectroscopy (SSNMR), powder X-ray diffraction (PXRD) and scanning electron microscopy–energy dispersive X-ray spectroscopy analysis (SEM–EDS). In addition, intrinsic dissolution rate experiments and solubility assays were performed. In the case of MET·HCl-HTZ (χMET·HCl = 0.66), we observed a slight enhancement in the dissolution properties compared with pure HTZ (1.21-fold). The same analysis for the solid forms of MET·HCl-CTZ (χMET·HCl = 0.33 and 0.5) showed an enhancement in the dissolved amount of CTZ accompanied by a slight improvement in solubility. From these dissolution profiles and saturation solubility studies and by comparing the thermodynamic parameters (ΔHfus and ΔSfus) of the pure drugs with these new solid forms, it can be observed that there was a limited modification in these properties, not modifying the free energy of the solution (ΔG) and thus not allowing an improvement in the dissolution and solubility properties of these solid forms.