The structure of ROH:R'OH heterodimers (R, R' = H, CH3, C2H5) trapped in argon and nitrogen matrixes was examined through two approaches: O-16/O-18 isotopic substitution in water and methanol and infrared-induced isomerization. Isotopic substitution clearly shows that in N-2 matrix the bigger molecule plays the role of proton donor (Type-I structure) and in Ar matrix that of proton acceptor (Type-II structure). This difference can be rationalized by considering the existence of weak OH...N-2 hydrogen bonds stabilizing the less stable structure. Selective irradiations in the vOH region were carried out for the CH3OH:H2O and C2H5OH:H2O dimers. Type-I --> Type-II interconversion was observed in N-2 matrix while no effect was detected in At. Finally the hydrogen bond strength evolution within the nine ROH:R'OH homo- and heterodimers was examined on both experimental and theoretical grounds. Experimentally this evolution was followed by considering the vOH frequency shifts of the proton donor subunit. Theoretically ab initio calculations of the structures, energies, and harmonic frequencies were performed in the DFT approach. In both cases for a given proton donor the frequency shift with respect to the monomer increases with the basicity of the proton acceptor (i.e. in the order H2O < CH3OH < C2H5OH); similarly, for a given proton acceptor, it increases with the acidity of the hydroxyl group (i.e. in the order C2H5OH < CH3OH < H2O). One exception, the C2H5OH:CH3OH Type-I heterodimer, for which the vOH shift of ethanol does not follow these rules, is experimentally observed. On the other hand the calculated dissociation energies and O...O distances also correctly vary according to the basicity of the proton acceptor and the acidity of the proton donor.