We present one of largest studies to date of combined near-infrared and submillimeter linear polarization data for a giant molecular cloud. The dust polarized emission data (at 250, 350 and 500 μm) were obtained using the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol) during its 2012 Antarctic flight. The near-infrared polarization, which is produced by dichroic extinction of background starlight, was measured in the I band (0.8 μm) using the Pico dos Dias Observatory in Brazil. The study targets the Vela C cloud, a conspicuous star-forming environment at a distance of approximately 700 pc, hosting HII regions, protostars, and dense filamentary structures. By studying the relationship between polarized emission and polarized absorption, we can investigate how this relates to the physical properties of dust grains. The area of overlap of the two data sets corresponds to a large fraction of the molecular cloud (approximately 1.5° × 2.0°), with hundreds of combined polarization pseudo-vectors distributed mainly along the borders of the cloud. For most sight-lines, the inferred magnetic field orientations match within 20°. Visual extinction values (AV) for near-infrared pseudo-vectors are estimated from 2MASS photometry. Based on these extinction values, we determine and correct for a small foreground contribution (~0.4%) in the near-infrared sample. We calculate the polarization efficiency ratio, defined as the polarization fraction at 500 μm divided by the polarization efficiency in the near-infrared (defined as P/AV). Models of aligned dust grains are helpful for producing predicted polarization maps from numerical simulations of turbulent molecular clouds, and the polarization efficiency ratio provides a constraint for such dust alignment models. Preliminary results show that the measured polarization efficiency ratio appears to be roughly consistent with the predictions of the Draine and Fraisse (2009) models.