Bill,
We went through the same thing back in June. The jasmine has been planted as a ground cover back 10 years ago or so. It became entanged in every single shrub, was climbing the walls at a rate of several inches a day, getting into windows, etc. We finally declared war on it. I used the kind of roundup made for woody vines and poison ivy, mixed at triple strength. It kinda turned the leaves a little brown, but not really a good quick kill. If you do it once a week or so, maybe after a few months you might have some success. Unfortunately, the only real solution, based on my experience, is to pull them and till the soil, after trimming them down to the ground with a HD weedeater. Then you will still have to keep pulling up new sprouts as you see them.
Our final solution was to rip out every shrub and plant in our front flowerbeds, including the jasmine. The original owner had made a poor selection of shrubs and had them planted too close to each other. We had some climbing rosebushes that I HATED (the wife loved them) that had also gotten out of control. I just hired a landscaping crew to clean everything out to the bare soil; we are starting over with a whole new look. Lots of rocks, flagstone, and carefully selected plantings widely spaced, etc. Oh yea, with MULCH instead of that horrid jasmine.
Good luck.
Steve