Do you put a comma after an introductory clause if it's a part of a dependent clause?
In your example, you don't actually have three clauses. Your primary sentence is "I knew that we could still work through it."
"...although he had a problem..." is the only secondary clause in the example. You could put it at the beginning or the end of the sentence, or in the middle as you did. It needs to be demarcated by commas, wherever you put it. If you put it in the middle, as you did, you need two commas. So it should really be:
I knew that, although he had a problem, we could still work through it.