  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 two
distinct situations, with the standard 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.
