A long time ago I read about using two spading forks back to back to pry apart plants in the garden. I've used this same idea to separate plants in pots only using smaller gardening tools and even kitchen forks.

You need to get the plants well-watered to start.... like the night before. If you can get the whole works out of the pot all the easier. Get your "forks" back to back )( between the roots of two plants and pull apart. There will be some root loss, but you'll be surprised how well this technique works.

Have your pots ready for replanting and the pot well watered. Take the entire mess out of the pot. Spray the roots with the hose to wet the roots and wash away the soil that's in there. Have you ever noticed how weeds are much easier to pull after a rain, that's what you are going for.

Then gently tease them apart, spraying again as needed. You will have some root loss because it is probably one big mess in there, but as long as each plant has a some root they will be ok. You might want to give them a haircut so the plant can repair it's roots and not have so much top to support. Otherwise they will be pretty droopy after transplanting.

It is not a good thing to have basil and parsley together. Basil is an annual and has roots that spread out. Parsley is a biennial and has a tap root like a dandilion.