  Chiral superconductors support chiral edge modes and potentially spontaneous
edge currents at their boundaries. Motivated by the putative multiband chiral
p-wave superconductor Sr$_2$RuO$_4$, we study the influence of the interference
between different bands at the edges, which may appear in the presence of
moderate edge disorder or in edge tunneling measurements. We show that
interband interference can strongly modify the measurable quantities at the
edges when the order parameter exhibits phase difference between the bands.
This is illustrated by investigating the edge dispersion and the edge current
distribution in the presence of interband mixing, as well as the conductance at
a tunneling junction. The results are discussed in connection with the putative
chiral p-wave superconductor Sr$_2$RuO$_4$. In passing, we also discuss similar
interference effects in multiband models with other pairing symmetries.
