ABSTRACT We compare the structure of synthetic dust polarization with synthetic molecular line emission from radiative transfer calculations using a three-dimensional, turbulent collapsing-cloud magnetohydrodynamics simulation. The histogram of relative orientation (HRO) technique and the projected Rayleigh statistic (PRS) are considered. In our trans-Alfvénic (more strongly magnetized) simulation, there is a transition to perpendicular alignment at densities above ∼4 × 103 cm−3. This transition is recovered in most of our synthetic observations of optically thin molecular tracers; however, for 12CO it does not occur and the PRS remains in parallel alignment across the whole observer space. We calculate the physical depth of the optical depth τ = 1 surface and find that for 12CO it is largely located in front of the cloud mid-plane, suggesting that 12CO is too optically thick and instead mainly probes low-volume density gas. In our super-Alfvénic simulation, the magnetic field becomes significantly more tangled, and all observed tracers tend towards no preference for perpendicular or parallel alignment. An observable difference in alignment between optically thin and optically thick tracers may indicate the presence of a dynamically important magnetic field, though there is some degeneracy with viewing angle. We convolve our data with a Gaussian beam and compare it with HRO results of the Vela C molecular cloud. We find good agreement between these results and our sub-Alfvénic simulations when viewed with the magnetic field in the plane of the sky (especially when sensitivity limitations are considered), though the observations are also consistent with an intermediately inclined magnetic field.