We calculate here the energy spectrum of InAs/GaSb heterostructure taking into account a complicated, anisotropic, and nonparabolic structure of the valence band of GaSb. In InAs/GaSb heterostructures the valence band of the GaSb layer overlaps with the conduction band of the InAs layer. The electrons in the InAs layer are coupled to the holes in the GaSb layer and a hybridization gap is formed. The coupling is considered here as a small perturbation for the problem of two decoupled infinite quantum wells, one of holes and one of electrons. The band structure of the coupled system shows features that result from anisotropy, dependence of the coupling on the in-plane vector, and lifting of the double degeneracy of the energy bands of electrons and holes due to the coupling. The splitting of the energy bands is very important at the crossing point. Interesting results of these effects are the possibility of a new kind of a gapless state and nontrivial constant energy contours.