Aims: Our aim is to obtain more information about the physical nature of B-type asteroids and extend previous work by studying their physical properties as derived from fitting an asteroid thermal model to their NASA's Wide-field Infrared Survey Explorer (WISE) data. We also examine the Pallas collisional family, a B-type family with a moderately high albedo in contrast to the large majority of B-types. Methods: We applied a combination of the near-Earth asteroid thermal model and a model of the reflected sunlight to WISE asteroid data in order to derive up to four parameters: effective diameter (D), the so-called infrared beaming parameter (η), ratio of infrared to visible albedo (Rp = pIR/pV), and visible geometric albedo (pV). Results: We obtained the effective diameter, geometric visible albedo, infrared-to-visible albedo ratio, and beaming parameter for ≳ 100 B-types asteroids and plotted the value distributions of pV, Rp, and η (p̅V = 0.07 ± 0.03, R̅p = 1.0 ± 0.2, and η̅ = 1.0 ± 0.1). By combining the IR and visible albedos with 2.5 μm reflectances from the literature we obtained the ratio of reflectances at 3.4 and 2.5 μm, from which we found statistically significant indications that the presence of a 3-μm absorption band related to water may be commonplace among the B-types. Finally, the Pallas collisional family members studied (~50 objects) present moderately high values of pV, p̅V = 0.14 ± 0.05, which is significantly higher than the average albedo of B-types. In addition, this family presents the lowest and most homogeneously distributed Rp-values of our whole sample, which shows that this group is clearly different from the other B-types, probably because its members are fragments likely originating from the same region of (2) Pallas, a particularly high-albedo B-type asteroid. Tables 1, 4, and Appendices A and B are available in electronic form at http://www.aanda.org