Two topics of high current interest in the field of unconventional superconductivity are non-centrosymmetric superconductors and multiband superconductivity. Half-Heusler superconductors such as YPtBi exemplify both. In this paper, we study bulk and surface states in nodal superconducting phases of the half-Heusler compounds, belonging to the $A_1$ ($s+p$-like) and $T_2$ ($k_zk_x+ik_zk_y$-like) irreducible representations of the point group. These two phases preserve and break time-reversal symmetry, respectively. For the $A_1$ case, we find that flat surface bands persist in the multiband system. In addition, the system has dispersive surface bands with zero-energy crossings forming Fermi arcs, which are protected by mirror symmetries. For the $T_2$ case, there is an interesting coexistence of point and line nodes, known from the single-band case, with Bogoliubov Fermi surfaces (two-dimensional nodes). There are no flat-band surface states, as expected, but dispersive surface bands with Fermi arcs exist. If these arcs do not lie in high-symmetry planes, they are split by the antisymmetric spin-orbit coupling so that their number is doubled compared to the inversion-symmetric case.
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