We calculate the electronic states of AlxGa1-xAs/GaAs/AlxGa1-xAs double heterojunctions subjected to a magnetic field parallel to the quasi-two-dimensional electron gas layer. We study the energy dispersion curves, the density of states, the electron concentration and the distribution of the electrons in the subbands. The parallel magnetic field induces severe changes in the density of states, which are of crucial importance for the explanation of the magnetoconductivity in these structures. However, to our knowledge, there has been no systematic study of the density of states under these circumstances. We attempt a contribution in this direction. For symmetric heterostructures, the depopulation of the higher subbands, the transition from a single-layer to a bilayer electron system and the domination of the bulk Landau levels in the centre of the wide quantum well, as the magnetic field is continuously increased, are presented in the `energy dispersion picture' as well as in the `electron concentration picture' and in the `density-of-states picture'.