The House card discarded by Patchface stays in the discard pile, all other cards are returned to the non-Baratheon players hand.
I don't believe that an official answer exists for this situation, as noted here in this BGG thread. I believe that a literal reading of the rules leads to a definitive answer. Important information of note from the rule book (page 19), under 3. Choose and Reveal House Cards:
"Playing a House card during combat is mandatory. Both attacker and defender must play a card." (rule book, page 19)
"At the end of a combat, if a player used his last (i.e., seventh) House card, he then returns the other six House cards currently in his discard pile to his hand. The last played card remains in the discard pile."
"Note: All House cards, whether available or used (i.e., discarded), are public knowledge. As such, a player’s discard pile or hand may be examined by others players at any time except during Step 3 of combat.
From the rules, I agree that you must pick up six House Cards, otherwise it would be impossible to satisfy the mandatory playing of a house card during the next combat (1st rule quote). The rules indicate using your seventh House card as the only rule (besides card rules text, like that of Roose Bolton) that makes you eligible to pick up the other six House cards in your discard (2nd rule quote). Luckily, the rules define two possible statuses for House cards, available or used (i.e. discarded) (emphasis mine) (3rd rule quote).
From the FAQ1.0 2nd Edition, we know that Patchface's ability applies after a player would pick up their six other cards, after playing their seventh. Since the non-Baratheon player isn't playing their last card though, the sixth card (played by the non-Baratheon player) is discarded, then Patchface discards their seventh and last card, making the non-Baratheon player pick up all their other cards including the House card played this combat. The House card discarded by Patchface stays in the discard pile.
Q: If a House card’s text ability says “after combat...,” when is that card resolved?
A: At the end of the Combat Clean Up step of Combat Resolution (after played House cards are discarded to their respective discard piles).
Q: If the Baratheon player plays his “Patchface” House card but his opponent is playing his last remaining House card, does the Baratheon player still get to discard one of his opponent’s House cards?
A: Yes, Patchface’s text ability would allow the Baratheon player to discard one of his opponent’s six House cards at the end of the Combat Clean Up step.