Polarized emission from aligned dust is a crucial tool for studies of magnetism in the ISM and a troublesome contaminant for studies of CMB polarization. In each case, an understanding of the significance of the polarization signal requires well-calibrated physical models of dust grains. Despite decades of progress in theory and observation, polarized dust models remain largely underconstrained. During its 2012 flight, the balloon-borne telescope BLASTPol obtained simultaneous broad-band polarimetric maps of a translucent molecular cloud at 250, 350, and 500 microns. Combining these data with polarimetry from the Planck 850 micron band, we have produced a submillimeter polarization spectrum for a cloud of this type for the first time. We find the polarization degree to be largely constant across the four bands. This result introduces a new observable with the potential to place strong empirical constraints on ISM dust polarization models in a previously inaccessible density regime. Comparing with models by Draine and Fraisse (2009), our result disfavors two of their models for which all polarization arises due only to aligned silicate grains. By creating simple models for polarized emission in a translucent cloud, we verify that extinction within the cloud should have only a small effect on the polarization spectrum shape compared to the diffuse ISM. Thus we expect the measured polarization spectrum to be a valid check on diffuse ISM dust models. The general flatness of the observed polarization spectrum suggests a challenge to models where temperature and alignment degree are strongly correlated across major dust components.