The newly developed Brillouin microscopy is used for the first time to measure in situ the longitudinal elastic stiffness coefficient in the GHz-range inside of glass-epoxy-metal joints as a function of distance from the substrates. Interphases with a local variation of mechanical properties are quantitatively characterized. These interphases possess unexpected widths of tens to hundreds of microns. Inside the interphases, the spatial variation of the longitudinal stiffness coefficient depends on the type of substrate, on the curing conditions for the epoxy and probably on the distribution of internal stresses. The obtained spatial mechanical profiles provide valuable insight into the morphology-driven mechanics of the interphase, but additional information is needed for a full understanding of their physical and chemical origin. The presented results prove the sensitivity of the Brillouin microscopy; the elastic stiffness coefficients are detected with an accuracy in the subpercentage range. The spatial resolution is better than 10 mum.