done with vs through with

done with and through with both are adjectives.

Word	Noun	Adjective	Verb	Adverb
done with	No	Yes	No	No
through with	No	Yes	No	No

As adjectives, done with and through with are synonyms defined as:

done with (adjective)	through with (adjective)
having no further concern with	having no further concern with
	having finished or arrived at completion