"Thank you, they are very well."
Translation:Grazie, stanno benissimo.
This link has an useful discussion: http://forum.accademiadellacrusca.it/forum_12/interventi/5219.shtml (in Italian). As stated in the quote, stare is often used when describing behaviour and feeling, and the two are at times interchangeable; I suspect that the distinction is more idiomatic than grammatical though. In my opinion, one rule is that when the predicate is an adverb (they are well) you should use stare (stanno bene), and when it's an adjective (they are nervous) you should use essere (sono nervosi). There are probably exceptions; I can only guarantee that "sono benissimo" sounds very wrong to an Italian ear.
Check out this site for a helpful breakdown: https://serenaitalian.wordpress.com/2010/09/09/difference-between-stare-and-essere/