I think prostrate is the proper term. They work well in front of windows and in a mixed flower bed. My red meidilands will throw long canes that poke through silver sage and lambs ears or hollies and make it appear that the blooms belong to them. Good for Banks and ditches.

Maybe try Karl's idea of putting down cardboard and then mulch just after planting to block the weeds from being pesty under the roses. The ones I have seen at Descanso near Pasadena were magnificent in full bloom.

I use organic methods and means only, and I plant groundcovers to discourage weeds, mostly violets, I bought several Victorian era violets from Canyon Ranch to plant beneath my O.G.R.s, and they formed a tight mat that kept weeds from spreading. Here each violet plant grows to be a mound of 1 foot X 1 foot and then they spread by sending runnners underground, to form a carpet. Although snails love to munch on violets, they are easily controlleld with iron pellets, I use "Sluggo", in spring and summer.
Berkeley Horticulture nursery recently started selling a corn product that is said to prevent weeds from sprouting. The documentation I read about it seemed promising, but I didn't keep it, sorry.

Luxrosa.

My mother had a serious thing for periwinkle (Vinca minor), and in the Philadelphia area, I completely understand that. I think periwinkle in that part of the world would work quite nicely as the ground cover for any rose bed.

I'll look into other plants such as Periwinkle as ground covers. At least they don't have thorns. Thornless rose GC's ,might be a good requirement in choosing one.