  We measure higher partial wave Feshbach resonances in an ultracold mixture of
fermionic $^6$Li and bosonic $^{133}$Cs by magnetic field dependent atom-loss
spectroscopy. For the $p$-wave Feshbach resonances we observe triplet
structures corresponding to different projections of the pair rotation angular
momentum onto the external magnetic field axis.
  We attribute the splittings to the spin-spin and spin-rotation couplings by
modelling the observation using a full coupled-channel calculation. Comparison
with an oversimplified model, estimating the spin-rotation coupling by
describing the weakly bound close-channel molecular state with the perturbative
multipole expansion, reveals the significant contribution of the molecular
wavefunction at short internuclear distances. Our findings highlight the
potential of Feshbach resonances in providing precise information on short- and
intermediate-range molecular couplings and wavefunctions. The observed $d$-wave
Feshbach resonances allow us to refine the LiCs singlet and triplet
ground-state molecular potential curves at large internuclear separations.
