Deep Space 9
In 2372, he was on board the Defiant when it rendezvoused with a Karemma starship in the Gamma Quadrant. When two Jem'Hadar attack ships attacked the Karemma, they tried to escape by entering the atmosphere of a nearby gas giant. The Defiant followed the ships into the atmosphere where it was fired upon and severely damaged. Chief Miles O'Brien sent Muniz to a Jefferies tube to assist Jadzia Dax. When the internal force fields began to collapse in that section, Muniz managed to get out, but Jadzia was left behind.
Muniz later returned to engineering to help O'Brien and Stevens to repair the ship. When Lieutenant Commander Worf arrived to take command of the ship after Captain Sisko, he criticized Muniz and Stevens. O'Brien reminded him that neither of them had attended Starfleet Academy and were not used to be commanding a starship. Stevens and Muniz later came up with a way to modify the deflector array to turn it into a phaser emitter. Their plan worked and the Jem'Hadar ship was destroyed. (DS9: "Starship Down")
In early-2373, Muniz was part of a Starfleet survey team from DS9 that traveled to the Gamma Quadrant planet Torga IV to assess the possibility of establishing a mining operation to extract some of the planet's rich deposits of cormaline. A Dominion ship crashed on the planet and was later followed by another who destroyed the team's runabout and landed Jem'Hadar troops. Muniz was wounded by the Dominion weapons, but was saved by O'Brien and Worf and taken into the ship. The anti-coagulant in the Dominion weapons soon took their toll on Muniz and his bleeding continued.
O'Brien and Worf clashed after Worf told him that Muniz was near death. As time went on, Muniz soon lost feeling in his legs and became delusional, believing he was watching a carnival with his father. Muniz eventually died of his wounds during the crew's attempt to use the ship's engines to escape.
After the Defiant arrived, rescued the crew and towed the Dominion ship off the planet and back to the Alpha Quadrant, Muniz's body was put into a torpedo casing and placed in the Defiant's cargo bay with O'Brien sitting with Muniz's body, performing a traditional Irish wake. He was joined by Worf who apologized for interrupting the Chief in his musings, but the Chief was not bothered by Worf's entrance. Upon seeing what the Chief was doing, he commented on its similarities to the old Klingon tradition of ak'voh. Both officers then proceeded to observe a vigil over the body together.
The script for "Starship Down" describes Muniz as simply, "a young enlisted engineer". Of a scene in the Defiant's engine room, it makes note of the fact Muniz and the other engineering crewmen didn't go to Starfleet Academy, saying, "they're not as polished as our people, and they have their own work habits and codes of behavior." 
In the script for "The Ship", Muniz is further described as, "a young Human crewman with an easy, infectious smile." 
The choice of bringing back Muniz for "The Ship" was an important one for the writing staff but looking back, they didn't think it quite worked out the way they had hoped. "Ira [Steven Behr] wanted to establish that there was an inner circle amongst the engineers, guys who hung out together," said writer Hans Beimler, "and that there was a special place in the heart of O'Brien for his engineering guys. Muniz was one of those guys. We tried to build a relationship between the two of them at the beginning." Commenting on that relationship, Behr explained, "The whole idea was to show that the engineers, the tech guys, have a brotherhood that's different from just the old Starfleet brotherhood. We wanted to bond O'Brien with this guy and have it mean something. But the scenes didn't play like two guys who were really comfortable with each other. It wound up being about O'Brien and a guy who's dying. The audience never came to care enough about Muniz because they didn't see O'Brien's investment in Muniz." (Star Trek: Deep Space Nine Companion, p.371)
Muniz appears in the Prophecy and Change short story "The Orb of Opportunity" which states he was a part of Chief O'Brien's team aboard the USS Orinoco which assisted Kai Winn Adami and General Lenaris Holem in their search for a blindvault that held the Orb of Contemplation.