Context. Dynamically, 133P/Elst-Pizarro and 176P/LINEAR are main belt asteroids, likely members of the Themis collisional family, and unlikely of cometary origin. They have been observed with cometary-like tails, which may be produced by water-ice sublimation. They are part of a small group of objects called Main Belt Comets (MBCs, Hsieh & Jewitt 2006). Aims: We attempt to determine if these MBCs have spectral properties compatible with those of comet nuclei or with other Themis family asteroids. Methods: We present the visible spectrum of MBCs 133P and 176P, as well as three Themis family asteroids: (62) Erato, (379) Huenna and (383) Janina, obtained in 2007 using three telescopes at "El Roque de los Muchachos" Observatory, in La Palma, Spain, and the 8 m Kueyen (UT2) VLT telescope at Cerro Paranal, Chile. The spectra of the MBCs are compared with those of the Themis family asteroids, comets, likely "dormant" comets and asteroids with past cometary-like activity in the near-Earth (NEA) population. As 133P was observed active, we also look for the prominent CN emission around 0.38 μm typically observed in comets, to test if the activity is produced by the sublimation of volatiles. Results: The spectra of 133P and 176P resemble best those of B-type asteroid and are very similar to those of Themis family members and another activated asteroid in the near-Earth asteroid population, (3200) Phaethon. On the other hand, these spectra are significantly different from the spectrum of comet 162P/Siding-Spring and most of the observed cometary nuclei. CN gas emission is not detected in the spectrum of 133P. We determine an upper limit for the CN production rate Q(CN) = 1.3 × 1021 mol/s, three orders of magnitude lower than the Q(CN) of Jupiter family comets observed at similar heliocentric distances. Conclusions: The spectra of 133P/Elst-Pizarro and 176P/LINEAR confirm that they are likely members of the Themis family of asteroids, fragments that probably retained volatiles, and unlikely have a cometary origin in the trans-Neptunian belt or the Oort Cloud. They have similar surface properties to activated asteroids in the NEA population, which supports the hypothesis that these NEAs are scattered MBCs. The low Q(CN) of 133P means that, if water-ice sublimation is the activation mechanism, the gas production rate is very low and/or the parent molecules of CN present in the nuclei of normal comets are much less abundant in this MBC.