I have a 3D valentine complete with shells and lace that I had framed between two pieces of glass. It is about 2 inches thick and can be rotated to show both sides. The valentine is hanging on fishing line between the glass.
It was not cheap to frame but well worth it.
I suggest doing something comparable: mount it on some good acid free paper or cotton fabric (tack it yourself) and stretch the fabric over something rigid. Put glass a half inch or so away from the fabric. Attaching it will prevent it from sagging. Ask a good framer for some suggestions.