Balmafula is an Arc Witch. This means that she is a reincarnated witch who contracts with the power of darkness. She is able to equip knives, robes, clothes, and accessories.

Zalmo, if equipped with a sword, is able to use a few Magic Sword abilities, but we never see him equipped with a sword.

Swords can be used by anyone that knows how to use them. Ignoring the job changing aspect of the game, I wouldn't be surprised if a lot of the main characters knew how to wield a sword aside from the Clerics. Rafa is seen holding a sword when she goes after the assassins on the roof, and Balmafula gets out a knife when she tries to fight against Delita.

That being said, out of all the playable characters, Teta, Alma, and Ovelia were probably the most out of place on the battlefield. They did not have any battle training at all and this is probably the reason Alma says that she wishes she was born a man, so that she could actually fight alongside Ramza.