I
think it's a
brocade (which is another type of jacquard), but I'm not sure. Brocade often has long floats, but I believe (as in the example we show in the fabric resource), floats are sometimes woven in, so the reverse is a solid fabric, rather than one with noticeable floats.
What's usual is the
ribbed texture of the black background to the motifs. I'm wondering if it's a type of ottoman or bengaline, but I can't quite see what's going on - maybe you can see more clearly. So perhaps a kind of combo of brocade / on a ground of a horizontal ribbed fabric such as bengaline.
This doesn't strike me as a truly reversible in the way a damask is. You do see the pattern on the back of a brocade, but not as an exact mirror image.
The ribbed section is not showing on the back which is why I think this doesn't meet the definition of damask, which would have the same weave showing on the reverse side, but in a mirror image of the front.
I'm no fabric expert though.
Looks like a wonderful dress!