It is shown that usually used theoretical model for double-layer heterostructures as a pseudospin ferromagnet does not explain the observed two-dimensional spectrum. Its existence is possible when neglecting Coulomb interaction destroying two-dimensional structures and can be realized only in a strong magnetic field. That is connected also with the plain vortex lattices forming in strong magnetic fields due to thermodynamic instability. This model gives reasonable explanations of various observed effects depending on the filling of the corresponding bands. In particular in this work we show that in double-layer heterostructures a large interlayer conductance really observed can exist.