Observations of prominence regions in hot coronal lines (≳106K) at wavelengths below the hydrogen Lyman absorption limit show what appear to be absorption features. Other authors have suggested that these observed features may be due to H and He continuum absorption. But there has, as yet, been no conclusive evidence that this is indeed the case. In this paper we present new Solar and Heliospheric Observatory (SOHO) observations that allow us to address this problem in a quantitative manner. We find that continuum absorption is the best explanation for the absorption observed in imaging data from the Coronal Diagnostic Spectrometer (CDS) on board SOHO. Furthermore, we discuss a new technique to measure the column depth of neutral hydrogen in a prominence, and use it to obtain estimates of the prominence filling factors as well. We calculate the column depth of neutral hydrogen, ξH ∼ 1018 cm−2, and the filling factor, f ≳0.3.