Every groundcover I've ever used creeps over mulch--Delosperma, several varieties of Geranium macrorhizum, Rubus Calycinoides, Arctostaphylos uva--ursi, Yellow creeping Jenny, a number of sedums, creeping thymes, etc.

The only groundcover I've had problems with as far as mulch goes is ajuga. Get any on the crown and it rots out.

I have had issues with blue star creeper climbing up into heathers and dwarf conifers and causing damage. Really like it otherwise....

All of my groundcovers creep on top of mulch. (I think they like it). It's not a problem to remove them and to root the little plants elsewhere or to give them away. I think that the mulch holds moisture & drains well & gives the creeping plants a good surface to spread on.
Susan

I agree. Most seem to creep over mulch. One plant, amazingly low, perhaps invasive, only briefly flowering, and evergreen, in zone 7, is Mazus repens. I only grow the white form, but the pale pink-purple sort is more easily found.