I checked my stats the other day and discovered that that was the subject of a search that brought a visitor to this blog. Short answer, you can combine any herb that you want with any other herb that you want. Long answer, you may not like the resulting flavor that you impart to your foods.
The world of cooking is constantly changing and new combination’s are tried every day. In fact there is no law against putting different herbs together. The more important thing is do they taste good when they are combined, for my taste-buds Dill and Tarragon would not be a good mix.
Both of them are strong flavoring agents. Both of them have distinctive flavors that tend to over-power everything else. Why are Dill pickles so popular, every “Deli” that I’ve ever been to serves one along with your sandwich. Tarragon is the same way even after it is reduced in red-wine vinegar it is a powerful flavoring agent in Bearnaise sauce. The thing is that some herbs are so powerful that the tastes will conflict with each other.
I enjoy tarragon on my salad, in a vinaigrette form. It makes an awesome addition to a crushed potato chip coating for fried chicken. It also is quite tasty when mixed in a cream sauce for bay scallops. On the other hand dill flavored chicken would not be an exciting taste for me, much less mixing it with tarragon in a cream sauce for scallops.
Italian herbs are so called because they do blend together, so Thyme, Basil, Oregano, Savory, Sage, Marjoram and Rosemary will combine together quite nicely. These are usually found in a tomato based sauces, though not always. The key thing is to find the blend that works best for the taste you are trying to achieve. If you add too much oregano to a tomato style sauce you will be rewarded with a taste that will be bitter, on the other hand for my taste an overdose of basil will just make the sauce better.
The whole point to using herbs is that the particular taste they impart is the exact flavor you are seeking. Bouillabaisse would not be Bouillabaisse with out saffron. A great Minestrone soup is really delightful with the addition of flowers from the zucchini, these impart a subtle flavor that you would not want to cover up or overpower with too much rosemary or other “Italian” herb. The point of using herbs is to learn to be “gentle” letting the subtle flavors just give you hints of bouquet with hitting you over the head.
So the long and short of it is that you need to go and find out for yourself if a certain combination of herbs will go together. Here is my list of strong flavored herbs that are best standing alone if you want a dominant taste. These can be combined in moderation in some cases when you are looking for a unique taste. If you add too much of any one, you will overpower the others or wind up with something that is just plain weird tasting.
Dill, Tarragon, Saffron, Mustard, Anise, Horseradish and of course any pepper when used in over abundance.
Your Mileage May Vary!
Update: I have seen this search come across 3 times now so I thought I would address it. Can you mix Cilantro and Mint? You bet! Actually; Thai cooks use a great deal of Basil, Cilantro and Mint combined in salads Rolled into spring rolls and for a mind-blowing taste try adding it to a fresh melon salad with honey-dew, cantalope, kiwi, strawberry and any other fruit you desire. The combination of those three herbs combined with the flavors of the fruit gives off a distinctly flowery type of taste that reminds me of eating violets it smells and tastes divine.
If you don’t have it yet you need to get The Flavor Bible After a few explanatory chapters the rest of the over three hundred pages is devoted to exploring the various combinations that herbs have been tried. along with some suggestions on the chemical affinities of the herbs that let you search for other combinations you can try for yourself. Get the physical book because you will find yourself trying to go 6 places in the book at one time and wanting to go back to the original page you started with.