The NEOWISE data set offers the opportunity to study the variations in albedo for asteroid classification schemes based on visible and near-infrared observations for a large sample of minor planets. We have determined the albedos for nearly 1900 asteroids classified by the Tholen, Bus, and Bus-DeMeo taxonomic classification schemes. We find that the S-complex spans a broad range of bright albedos, partially overlapping the low albedo C-complex at small sizes. As expected, the X-complex covers a wide range of albedos. The multiwavelength infrared coverage provided by NEOWISE allows determination of the reflectivity at 3.4 and 4.6 μm relative to the visible albedo. The direct computation of the reflectivity at 3.4 and 4.6 μm enables a new means of comparing the various taxonomic classes. Although C, B, D, and T asteroids all have similarly low visible albedos, the D and T types can be distinguished from the C and B types by examining their relative reflectance at 3.4 and 4.6 μm. All of the albedo distributions are strongly affected by selection biases against small, low albedo objects, as all objects selected for taxonomic classification were chosen according to their visible light brightness. Due to these strong selection biases, we are unable to determine whether or not there are correlations between size, albedo, and space weathering. We argue that the current set of classified asteroids makes any such correlations difficult to verify. A sample of taxonomically classified asteroids drawn without significant albedo bias is needed in order to perform such an analysis.