We investigate imaging of moiré structures in free-standing twisted bilayer graphene (TBG) carried out by transmission electron microscopy (TEM) in diffraction and in-line Gabor holography modes. Electron diffraction patterns of TBG acquired at typical TEM electron energies of 80-300 keV exhibit the diffraction peaks caused by diffraction on individual layers. However, diffraction peaks at the scattering angles related to the periodicity of the moiré structure have not been observed in such diffraction patterns. We show that diffraction on moiré structure can create intense diffraction peaks if the energy of the probing electrons is very low, in the range of a few tens of eV. Experimental diffraction patterns of TBG acquired with low-energy electrons of 236 eV exhibiting peaks attributed to the moiré structure periodicity are shown. In holography mode, the intensity of the wave transmitted through the sample and measured in the far-field can be enhanced or decreased depending on the atomic arrangement, as for example AA or AB stacking. Thus, a decrease of intensity in the far-field must not necessarily be associated with some absorption inside the sample but can simply be a result of a particular atomic arrangement. We believe that our findings can be important for exploiting graphene as a support in electron imaging.