We present both structural and vibrational (Raman) results of compressed xenon binary systems of He and H₂ to a maximum pressure of 142 GPa. In the He-Xe mixture 15% vol. Xe and balance He, we observe no evidence for van der Waals compound formation. Pure fcc Xe can be crystallised from the 2-phase Xe-He fluid at 0.6 GPa. The expected fcc-hcp transition is accompanied by extensive diffuse scattering and the emergence of hcp reflections at higher pressures. There is no apparent volume expansion of the measured Xe equation of state in helium indicating a near-zero (iso-structural) solubility of He in Xe. In the H₂-Xe system, X-ray diffraction revealed the presence of two solid-phase structures in a 15% by volume mixture, one of which was best indexed on an orthorhombic cell. Raman spectroscopic studies of both 15% and 7.5% Xe binary mixtures by volume in H₂, showed shifted vibron frequencies relative to the normal, pure (bulk) H-H stretch mode (vibron) that soften with pressure and appear to cross the pressure-frequency trajectory of the H₂ vibron. The 7.5 vol % Xe-H₂ mixture freezes at 5.3 GPa to a solid occupying the bulk of the available sample volume in the DAC, indicating a close-to-stoichiometric composition for one Xe-H₂ solid phase.