Polarized emission from aligned dust is a crucial tool for studies of magnetism in the ISM, but a troublesome contaminant for studies of cosmic microwave background 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 broadband polarimetric maps of a translucent molecular cloud at 250, 350, and 500 μm. Combining these data with polarimetry from the Planck 850 μm band, we have produced a submillimeter polarization spectrum, the first for a cloud of this type. 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. Compared to models by Draine & Fraisse, 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.