  We investigate the presence of vortices in generalized Maxwell-Higgs models
with a hidden sector. The model engenders $U(1)\times U(1)$ symmetry, in a
manner that the sectors are coupled via the visible magnetic permeability
depending only on the hidden scalar field. We develop a first order framework
in which the hidden sector decouples from the visible one. We illustrate the
results with two specific examples, that give rise to the presence of vortices
with internal structure.
