How can a molecular orbital with a nodal plane still be considered "bonding"?
The number of nodal planes isn't the determining factor. Yes, having more nodal planes increase the energy of the orbital, but you need to consider the fact that some MOs (specifically the anti bonding ones) are raised in energy. Overall, the total energy of the orbitals is the same as before, so you stabilize some and destabilize others. Take a look at the MOs and you can see that the there's two bonding MOs with one nodal plane perpendicular to the plane of the benzene with $E_{1}$ symmetry. Likewise, there's a pair of MOs with two nodal planes that with $E_{1}$ symmetry that are anti-bonding. These pairs happened to be correlated in that the increase in energy of the anti-bonding orbitals is essentially matched by the stabilization of the bonding orbitals.