Using the Planck Low Frequency Instrument (LFI) and WMAP data within the global Bayesian B EYOND P LANCK framework, we constrained the polarized foreground emission between 30 and 70 GHz. We combined, for the first time, full-resolution Planck LFI time-ordered data with low-resolution WMAP sky maps at 33, 40, and 61 GHz. The spectral parameters were fit with a likelihood defined at the native resolution of each frequency channel. This analysis represents the first implementation of true multi-resolution component separation applied to CMB observations for both amplitude and spectral energy distribution (SED) parameters. For the synchrotron emission, we approximated the SED as a power-law in frequency and we find that the low signal-to-noise ratio of the current data strongly limits the number of free parameters that can be robustly constrained. We partitioned the sky into four large disjoint regions (High Latitude; Galactic Spur; Galactic Plane; and Galactic Center), each associated with its own power-law index. We find that the High Latitude region is prior-dominated, while the Galactic Center region is contaminated by residual instrumental systematics. The two remaining regions appear to be signal-dominated, and for these we derive spectral indices of β s Spur  = −3.17 ± 0.06 and β s Plane  = −3.03 ± 0.07, which is in good agreement with previous results. For the thermal dust emission, we assumed a modified blackbody model and we fit a single power-law index across the full sky. We find β d  = 1.64 ± 0.03, which is slightly steeper than the value reported in Planck HFI data, but still statistically consistent at the 2 σ confidence level.