The electronic structure of the nanolaminated transition metal carbide Ti2AlC has been investigated by bulk-sensitive soft x-ray emission spectroscopy. The measured Ti L, C K and Al L emission spectra are compared with calculated spectra using ab initio density-functional theory including dipole matrix elements. The detailed investigation of the electronic structure and chemical bonding provides increased understanding of the physical properties of this type of nanolaminates. Three different types of bond regions are identified; the relatively weak Ti 3d - Al 3p hybridization 1 eV below the Fermi level, and the Ti 3d - C 2p and Ti 3d - C 2s hybridizations which are stronger and deeper in energy are observed around 2.5 eV and 10 eV below the Fermi level, respectively. A strongly modified spectral shape of the 3s final states in comparison to pure Al is detected for the buried Al monolayers indirectly reflecting the Ti 3d - Al 3p hybridization. The differences between the electronic and crystal structures of Ti2AlC, Ti3AlC2 and TiC are discussed in relation to the number of Al layers per Ti layer in the two former systems and the corresponding change of the unusual materials properties.