We studied effect of molecular interactions on the physical properties of binary freeze-dried solids and frozen aqueous solutions using model chemicals containing various functional groups (amino, carboxyl, hydroxyl). Thermal analysis of frozen solutions containing alkyl diamines and hydroxy di- or tricarboxylic acids showed thermal transitions (T_g′: glass transition of maximally freeze-concentrated phase) at temperatures higher than those of the individual solutes. A binary frozen solution containing 80 mM 1,3-diamino-2-hydroxypropane (single-solute T_g′<−60 °C) and 120 mM citric acid (single-solute T_g′: −55.0 °C) made the transition at −30.8 °C. The molecular weight of the solutes had smaller effects on the transition temperatures of the frozen mixture component solutions. Lyophilization of some high T_g′ mixture frozen solutions (e.g., 1,3-diamino-2-hydroxypropane and citric acid) resulted in cake-structure amorphous solids with glass transition temperatures (T_g) higher than those of the individual components. Networking of intense hydrogen-bondings and electrostatic interactions between the heterogeneous molecules through the multiple functional groups was suggested to reduce the component mobility in the amorphous freeze-concentrated phase and the freeze-dried solids. Controlling the interactions should be a key to optimizing the physical properties of multi-component amorphous freeze-dried pharmaceutical formulations.