Spotted spurge is my scourge, and a pre-emergent did not work. I pull over 200 small spurge plants per week. They grow both between the thyme and also right through very successful and thick thyme. Is there a post-emergent solution?
Herbicides Safe for Elfin Thyme
Certified GKH Gardening Expert
Unfortunately, every herbicide that I know of that kills spurge will also kill thyme. Most herbicides are targeted either at broadleaf plants, at grasses, or at both, and spurge and thyme are both broadleaf plants.
You could try pouring boiling water or vinegar on the spurge that's growing between the thyme, and repeating this several times. Since your thyme is well established, perhaps you could then mulch over all the exposed soil to suppress the spurge, while being extra careful to weed out the spurge that is growing in the theyme.
These articles give some additional ideas for killing weeds that may help: