We present a large-scale combination of near-infrared (near-IR) interstellar polarization data from background starlight with polarized emission data at submillimeter wavelengths for the Vela C molecular cloud. The near-IR data consist of more than 6700 detections probing a range of visual extinctions between 2 and 20 {mag} in and around the cloud. The submillimeter data were collected in Antarctica by the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry. This is the first direct combination of near-IR and submillimeter polarization data for a molecular cloud aimed at measuring the “polarization efficiency ratio” ({R}{eff}), a quantity that is expected to depend only on grain-intrinsic physical properties. It is defined as {p}500/({p}I/{τ }V), where p 500 and p I are polarization fractions at 500 μ {{m}} and the I band, respectively, and {τ }V is the optical depth. To ensure that the same column density of material is producing both polarization from emission and from extinction, we conducted a careful selection of near-background stars using 2MASS, Herschel, and Planck data. This selection excludes objects contaminated by the Galactic diffuse background material as well as objects located in the foreground. Accounting for statistical and systematic uncertainties, we estimate an average {R}{eff} value of 2.4 ± 0.8, which can be used to test the predictions of dust grain models designed for molecular clouds when such predictions become available. The ratio {R}{eff} appears to be relatively flat as a function of the cloud depth for the range of visual extinctions probed.