  This work deals with thick branes in bulk with a single extra dimension
modeled by a two-field configuration. We first consider the inclusion of the
cuscuton to also control the dynamics of one of the fields and investigate how
it contributes to change the internal structure of the configuration in three
distinct situations, with the standard, the modified and the asymmetric Bloch
brane. The results show that the branes get a rich internal structure, with the
geometry presenting a novel behavior which is also governed by the parameter
that controls the strength of the cuscuton term. We also study the case where
the dynamics of one of the two fields is only described by the cuscuton. All
the models support analytical solutions which are stable against fluctuations
in the metric, and the main results unveil significant modifications in the
warp factor and energy density of the branes.
