I checked my opponent with a bishop and he moved onto a square covered by my knight. He said that was ok because I could not take him with my knight as I would be moving myself into check as my knight was the only piece between his queen and my king. Was he correct in saying that?
No, your opponent is wrong. A king is not allowed to move onto a covered square.
If the opponent's king is trapped so that its escape is not possible, it is checkmate.
If the king is threatened with capture (check), the player must remove the threat of capture on the next move by moving onto an uncovered square.
If this is not possible, the king is said to be in checkmate and the game is over.
In your case your opponent's king is not allowed to move onto a square that is covered by your knight. The fact that your knight is pinned by your opponents queen does not matter at all.