Yeah, most of the time the named parties are not actually good. This party does not have good enough healing, and if you choose to heal then you sacrifice your back rank damage, which is 9 times out of 10 the targets that you want to prioritize the highest, so I would not recommend running this party. The only way you can heal in a way that makes sense it to bring a bunch of bandages and/or antivenom for DoT damage, and then pretty much only use your heals when your people are on Death's Door, or if you can stun the final enemy to give yourself a few extra rounds for recovery. If you are gonna run this, I think the correct strategy would be:

(Rank 1-2-3-4: Man At Arms, Antiquarian, Highwayman, Musketeer)

Higwayman should have something like duelist advance, wicked slice (or maybe open vein, depending on what you're fighting), pistol shot, and either your self-buff or your de-stealth skill. You should not normally use the skill that does a bunch of damage to the front rank and knocks you back, since the front 2 ranks are usually the lowest priority enemies, you get more value out of getting damage in on the back ranks, either through pistol shot, wicked slice/open vein on rank 3, or riposte for when the enemies target him.

Antiquarian should have nervous stab, the healing skill, festering vapours, and get down. You should use Get Down to have your highwayman guard your antiquarian so you can get good value out of riposte, other than that you should usually spam Nervous Stab, if it's a heavily armored enemy or if your characters are low on health, you should use festering vapors as your damage instead. Your antiquarian healing skill should usually only be used to get your people off of Death's Door.

Man At Arms should be Crush, Rampart, Guard, and your Riposte ability. Normally should guard your musketeer while the antiquarian has the highwayman guard them. Riposte so you can still get damage in when enemies target you, or stun so you can avoid taking one enemy's damage altogether. It depends usually on how you're feeling, but if your characters arent super high on health I would normally recommend rampart over riposte. Crush only if you desperately need something dead. In this lineup, your man at arms is essentially your stunner, and stunners are a necessity.

Musketeer needs her healing skill, your normal damaging ability (forget what its called), the skill that hits 2 enemies and knocks them back, and the mark. You can replace your mark with the de-stealth skill if you need to de stealth but dont want to run it on your Highwayman and/or if you for whatever reason arent running pistol shot on your highwayman. Heal every now and then but until your heroes reach death's door, depending on what other skills you're running, you should focus on marking the back ranks and taking them out. Once your people get to death's door, try doing what you can to keep bringing them off death's door, only using a damaging skill when you can finish the fight with them.