Free Form PbP. Writers take turns posting their actions towards and against each other, not calling hits, and allowing the other writer to receive damage as they see fit. All deaths must be agreed upon as no writer can kill another persons character. This protection from insta-death is rarely gifted towards 'Unnamed NPCs' however.
It is highly recommended that you PM your combat partner and talk the combat through too. Some examples of what to talk about are: your expectations, complicated movesets, rifle specifications, misunderstandings, complications, map positions, freedom of movement, environmental hazards, and even the complete resolution.
Seek a balance between working together and keeping it spontaneous. And keep in mind that balance is different for every writer.