Amyloid and amyloid-like fibrils are a general class of protein aggregates and represent a central topic in life sciences for their involvement in several neurodegenerative disorders and their unique mechanical and supramolecular morphological properties. Both their biological role and their physical properties, including their high mechanical stability and thermodynamic inertia, are related to the structural arrangement of proteins in the aggregates at molecular level. Significant variations may exist in the supramolecular organization of the commonly termed cross-β structure that constitutes the amyloid core. In this context, a fine knowledge of the structural details in fibrils may give significant information on the assembly process and on possible ways of tuning or inhibiting it. Here we propose a simple method based on the combined use of Fourier transform infrared spectroscopy and Fourier transform Raman spectroscopy to accurately reveal structural details in the fibrillar aggregates, side-chain exposure and intermolecular interactions. Interestingly, coupled analysis of mid-infrared spectra reveals antiparallel β-sheet orientation in ConA fibrils. We also report the comparison between THz absorption spectra of Concanavalin A in its native and fibrillar state at different hydration levels, allowing obtaining corroboration of peaks assignation in this range and information on the effect of amyloid supramolecular arrangement on the network dynamics of hydration water.