We investigate the presence of vortices in generalized Maxwell-Higgs models with a hidden sector. The model engenders $U\left(1\right)\times U\left(1\right)$ 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.