If there was a single class called the Martial class, you would most certainly be right. Such a class could not be designed to be both mundane or supernatural with or without magic items. The word, however, is an umbrella term that covers classes such as the Barbarian, Fighter, Monk, Paladin, Ranger and Rogue. With the exception of the Fighter and the Rogue, most of these classes have something supernatural. A Barbarian can pull off something supernatural whenever they rage. A Monk can use Ki to do something supernatural. The Ranger and the Paladin can tap into the primal or the divine to cast spells. The Fighter and the Rogue are mundane, but they can push themselves to the best they can be through training and skill. So some martial classes can be one or the other.
The OP's question could have been a little more specific.
Is a Barbarian, mundane or supernatural?
Is a Fighter, mundane or supernatural?
etc.