you can't counterspell them or antimagic field them
A Martial power cant be "counterspelled" because Martial powers are never a form of "spellcasting".
How a Martial power interacts with an antimagic zone is less obvious.
According to the
Antimagic Field spell: "This area is divorced from the magical energy that suffuses the multiverse. Within the sphere, spells cant be cast, summoned creatures disappear, and even magic items become mundane." These two sentences require inference to makes sense of.
The "Weave" is this magical energy that suffuses the multiverse. Magic is a mysterious quality of existence itself. (I compare it to the quantum observer effect. A weird quality of consciousness and existence.) The Weave is something different. The Weave is ambient magic, the background noise generated by magical properties of things. Arcane magic and divine magic rely on this free-floating residual magic.
The antimagic creates a void in the Weave, where there is no free-floating ambient magic. The spell description implies, spells rely on the Weave, the avatar of a summoned extraplanar creature relies on the Weave (!), and even the magicality of a magic item needs to plug into the Weave in order to function magically. Without the Weave fueling a magic item, it is effectively a mere mundane item.
Apparently, any spell is relying on the Weave to sustain its effect until the spell ends. Thus, an
Antimagic Field can "suppress" the effect itself (even after cast) while overlapping it. (It remains unclear why the fire of a
Fireball or a
Wall of Fire can explicitly be suppressed, while the water of a
Create Water probably cant?)
By extrapolation. Martial powers are magic. But they dont depend on the Weave.
Probably the magic is the aspect that is inherent in the existence of the Martial character, whether ones material body or immaterial soul, or wherever the magic derives from.