The stability of "visible"electroweak-type cosmic strings is investigated in an extension of the Standard Model by a minimal dark sector, consisting of a U(1) gauge field, broken spontaneously by a scalar. The visible and dark sectors are coupled through a Higgs-portal and a gauge-kinetic mixing term. It is found that strings whose core is "filled"with a dark scalar condensate exhibit better stability properties than their analogues in the Standard Model, when the electroweak mixing angle is close to θW=π/2. They become unstable as one lets θW approach its physical value. The instability mechanism appears to be a W-boson condensation mechanism found in previous studies on the stability of electroweak strings.