  We calculate the orbital magnetic susceptibility $\chi_{\mathrm{orb}}$ for an
8-band tight-binding model of gapless and gapped graphene using Green's
functions. Analogously, we study $\chi_{\mathrm{orb}}$ for a $\mathrm{MoS_2}$
12-band model. For both materials, we unravel the character of the processes
involved in the magnetic response by looking at the contribution at each point
of the Brillouin zone. By this, a clear distinction between intra- and
interband excitations is generally possible and we are able to predict
qualitative features of $\chi_{\mathrm{orb}}$ only through the knowledge of the
band structure. The study is complemented by comparing the magnetic response
with that of 2-band lattice Hamiltonians which reduce to the Dirac and
Bernevig-Hughes-Zhang (BHZ) models in the continuum limit.
