We present a large-scale combination of near-infrared (near-IR) interstellar polarization data from background starlight with polarized emission data at submillimeter (sub-mm) 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 sub-mm data was collected in Antartica by the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol). This is the first direct combination of near-IR and sub-mm polarization data for a molecular cloud aimed at measuring the polarization efficiency ratio ($R_{mathrm{eff}}$), a quantity that is expected to depend only on grain intrinsic physical properties. It is defined as $p_{500}/(p_{I}/tau_{V})$, where $p_{500}$ and $p_{I}$ are polarization fractions at $500,mu$m and $I$-band, respectively, and $tau_{V}$ 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 $R_{mathrm{eff}}$ value of $2.4pm0.8$, which can be used to test the predictions of dust grain models designed for molecular clouds when such predictions become available. $R_{mathrm{eff}}$ appears to be relatively flat as a function of the cloud depth for the range of visual extinctions probed.
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