Jordan-Schönflies Curve Theorem - Multiple Curves

Question

Jordan-Schönflies Curve Theorem states:

For any simple closed curve in the plane, there is a homeomorphism of the plane which takes that curve into the standard circle.

Question: Is there a similar theorem for finitely many non-intersecting simple closed curves?

For example, given two non-intersecting simple closed curves, is there a homeomorphism of the plane which takes the curves into two non-intersecting circles? There could be two cases:

1. One circle lies inside another circle;
2. No circle is contained in another circle.

I am trying to prove that if $U$ is a bounded open set whose topology boundary is a union $B$ of ranges of multiple non-intersecting simple closed curves, then $\overline{U}$ is a manifold with boundary whose manifold boundary is exactly $B$.