We have measured the zero-bias differential tunneling conductance of InAs/AlSb/GaS b/AlSb/InAs heterostructures at low temperatures (1.7K < T < 60K) and unde r a magnetic field at various angles with the heterostructures interfaces. Shubni kov-de Haas oscillations in the magnetoconductance reveal the two-dimensional (2D) character of the electrons accumulated at the InAs interfaces and yield their num ber in each of them. The temperature dependence of the oscillations suggests the f ormation of a field-induced energy gap at the Fermi level, similar to that observe d before in simpler 2D-2D tunneling systems. A calculation of the magnetoconductan ce that considers different 2D densities in the two InAs electrodes agrees with th e main observations, but fails to explain features that might be related to the pr esence of 2D holes in the GaSb region.