Parsley stems can be finely chopped into a cooked dish or dressing when they are tender enough. A rosemary branch is a different proposition; its woody center is usually something to remove after flavoring the food.
Inspect the herb rather than applying one rule to every bunch. Separate tough stems, wash as appropriate, and dry well before chopping. Wet leaves tend to clump and can dilute a delicate dressing.
Chop only what you need when possible. A handful of fresh leaves added at the end gives a different result from herbs simmered through a sauce. Both can be useful, but they should be deliberate.
If the remaining bunch is always forgotten, choose a second meal that uses it while it is still fresh. Buying an herb for one garnish and leaving the rest without a plan is an expensive way to decorate dinner.