Parts of "An Occurrence at Owl Creek Bridge" are narrated from a strictly objective point of view by what is customarily called a third-person omniscient narrator, presumably the author Ambrose Bierce himself. Other parts are narrated from the point of view of Peyton Farquhar and could be called an interior monologue, although the omniscient narrator might be said to have the power to go inside Farquhar's mind or anywhere else, as well as to go backwards and forwards in time.
The first section of the story begins with a completely objective description. For example:
A man stood upon a railroad bridge in northern Alabama, looking down into the swift water twenty feet below. The man's hands were behind his back, the wrists bound with a cord.
After describing the entire setting, including Farquhar himself, the narrator moves subtly into the protagonist's mind. The exact sentence where this transition occurs is:
He looked a moment at his "unsteadfast footing," then let his gaze wander to the swirling water of the stream racing madly beneath his feet.
The narrative remains in Farquhar's mind and his point of view almost to the end of the first section. Then the last short paragraph moves back into an objective point of view.
As these thoughts, which have here to be set down in words, were flashed into the doomed man's brain rather than evolved from it the captain nodded to the sergeant. The sergeant stepped aside.
Section II is short. It is a flashback in time to explain how Farquhar came to be standing on the railroad bridge with a noose around his neck. It is told from an objective point of view, i.e., from the outside. Much of the section is dramatized. Most of the dialogue is between Farquhar and the man masquerading as a Confederate soldier. The section ends with the ominous words:
He was a Federal scout.
Section III is told almost entirely from Farquhar's point of view. It is not literally what happened but what he is imagining. He imagines that the rope broke and he fell into the creek. Bierce has established that the creek is flooded, swirling, and moving swiftly. This would explain how Farquhar could be carried out of rifle range so quickly and would be hard to hit. The entire long section describes his thoughts and feelings and could be called "an internal monologue," but it could also be considered the prerogative of the omniscient narrator who can go backwards and forwards in time and into the mind of any character.
Section III delivers the shocking ending.The reader has been beguiled into believing that Farquhar has escaped hanging and is on his way back to his home, wife, and children. Then at the very end, when he is "about to clasp" his wife "he feels a stunning blow upon the back of the neck..." And the narrative move backwards in time to the Owl Creek bridge, where the end is told from a dispassionate, objective point of view.
Peyton Farquhar was dead; his body, with a broken neck, swung gently from side to side beneath the timbers of the Owl Creek bridge.
Everything that Peyton Farquhar had imagined, from the time he fell from the bridge to the time that his neck was broken by the rope, had gone through his mind in the few seconds it took for him to fall through the air before the slack in the rope was taken up and his dream of freedom came to an abrupt end. The words "swung gently from side to side" seem to emphasize the objectivity of the omniscient narrator, who is just describing the sight dispassionately.