I wouldn't use any pine bark mulch around herbs. The pine needles and bark tend to give off 'chemicals' that herbs don't like. The mulch is mainly to stop weeds from sprouting, so it shouldn't be used around herbs. Ever notice that not much grows under a pine tree?

Are there any herbs which DO like pine bark mulch, I wonder?

You and your herbs will be much happier with some sort of straw mulch. I use sugar-cane mulch because it's cheap and readily available where I live. Your local gardening centre/nursery will have several choices for you, and can advise on the best. Just make sure the mulch is well and truly dead and dry, and try to select one which doesn't have seeds in it.