  We use a hybrid k dot p theory - tight binding (HkpTB) model to describe
interlayer coupling simultaneously in both Bernal and twisted graphene
structures. For Bernal-aligned interfaces, HkpTB is parametrized using the full
Slonczewski-Weiss-McClure (SWMcC) Hamiltonian of graphite, which is then used
to refine the commonly used minimal model for twisted interfaces, by deriving
additional terms that reflect all details of the full SWMcC model of graphite.
We find that these terms introduce some electron-hole asymmetry in the band
structure of twisted bilayers, but in twistronic multilayer graphene, they
produce only a subtle change of moire miniband spectra, confirming the broad
applicability of the minimal model for implementing the twisted interface
coupling in such systems.
