  The conductance, the transmission and the reflection probabilities through
rectangular potential barriers and pn-junctions are obtained for bilayer
graphene taking into account the four bands of the energy spectrum. We have
evaluated the importance of the skew hopping parameters {\gamma}3 and {\gamma}4
to these properties and show that for energies E>{\gamma}1/100 their effect is
negligible. For high energies two modes of propagation exist and we investigate
scattering between these modes. For perpendicular incidence both propagation
modes are decoupled and scattering between them is forbidden. This extends the
concept of pseudospin as defined within the two band approximation to a four
band model and corresponds to the (anti)symmetry of the wavefunctions under
in-plane mirroring. New transmission resonances are found that appear as sharp
peaks in the conductance which are absent in the two band approximation. The
application of an interlayer bias to the system: 1) breaks the pseudospin
structure, 2) opens a bandgap that results in a distinct feature of suppressed
transmission in the conductance, and 3) breaks the angular symmetry with
respect to normal incidence in the transmission and reflection.
