The model of a domain wall ("thick brane") in noncompact five-dimensional space-time is considered with geometries of AdS type generated by self-interacting scalar matter composed of two fields with minimal coupling to gravity. The mixing of scalar and gravitational degrees of freedom leads to contributions to the invariant scalar fluctuations potential that remain nontrivial in the limit of turned off gravity. This leads to the disappearance of the Goldstone mode associated with translational symmetry breaking and to the different mass of the Higgs-like scalar state.