In Real Life wet navies, it does not work. Battleships and carriers require very different paradigms; the former are built for taking and dealing out heavy damage, which demands certain armor and armament characteristics, such as compartmentalization to minimize damage spread but also cut into holding space. Fighter landing strips, hangars and the stores for their fuel and munitions would detract from this role, leaving you with a Master of None that cannot fight or tank as well as a pure combatant or service as many fighters as a pure carrier. This didn't stop some attempts from being made. When initially launched in the late 1920s, the USS Lexington and Saratoga had a complement of cruiser-class 8-inch guns. Japan put similar 8-inch guns in casemates on the sides of Akagi and Kaga. The reasoning behind the guns was so they could defend themselves if ambushed at night or in bad weather when planes couldn't fly, but they proved to be generally useless - the necessary high speed of carriers was a better defense. Japan also created hybrid Battleship/seaplane carriers out of a couple of old battleships, Ise and Hyuga in the wake of losses at the Battle of Midway.
The naysayers turned out to be right: Ise and Hyuga were total failures, and the large guns on the US ships interfered with flight operations if actually used, and they were removed in 1942. The 8-inch casemates were going to be removed from Kaga and Akagi after Midway, but the ships were sunk first. Other experiments never got even this far. The sole modern attempt to revive this concept is the Russian "aircraft cruiser" Admiral Kuznetsov, and even that had its antiship missiles removed in a refit.
It was NOT obvious in 1920s - when 8-inch armed carriers were designed - because the capabilities and radius of planes weren't sufficient yet to allow carriers reliable standoff capabilities. Fast carriers were supposed to operate with cruisers/battlecruisers vanguard; the probability of them being dragged in surface action was significant (radars weren't invented yet, and aviation reconnaissance was still flawed). Also, carriers were - and still is - dependent on wind directions. They need to run into the wind to safely launch or land planes. And if the wind is from enemy directions, carriers are forced to toward the enemy, which seriously negate any standoff they may hope to have. In 1920s, when planes were short-legged, launch operations slow and time-consuming, and planes payload could not ensure the destruction of the enemy even if strike was launched in time - having heavy guns on carrier was a good way to ensure her survival.
It is worth noting that Real Life examples of this trope largely predate Real Life examples of dedicated aircraft carriers. Many early experiments in launching and recovering airplanes from warships involved cruisers and battleships, and the first aircraft carrier to launch a wartime air raid, the British HMS Furious, began life as a battlecruiser and went through various intermediary designs where she retained some of her main battery along with a flight deck. They wouldn't settle on the flush-deck carrier design modern viewers would recognize until the postwar period.
In space, however, this model is less silly than it might appear. A trio of points: First, given how planets move through space and the need for at least rudimentary slingshot orbits, trajectories are actually fairly predictable in time and space, therefore, combat is likely to be very short range, though you could send a bunch of missiles hurtling down this space "lane". Although fightercraft are less useful in a traditional role, they can bring weapons (e.g. missiles) closer, in under the target's point-defense range, and at this point in time we can't conceive of a spacecraft that could take a missile and keep fighting, but if we could take the missile out early, the most it could do could be irradiate the ship, and you can armor against that. You can actually make an argument for almost any weapon in space, though for kinetics you'd need a propellant that doesn't need outside air, and be willing to live with the fact that you're putting hyper-lethal debris somewhere, especially immediate if you're fighting in near-orbit. Thirdly, Deflector Shields could help mitigate some of the carrier's vulnerabilities, especially if physical Armor Is Useless such that pure battleships don't have superior durability after all.
Furthermore, depending on the Faster-Than-Light Travel system used by the work, the carrier strike group system used in Real Life may not work. In Real Life, enemy ships have to battle through fighter screens and escorts to get to the lightly-armored carrier. There has been but a grand total of two carriers lost to surface action, namely Glorious to the German battlecruisers Gneisau and Scharnhorst, due in no small part to her captain's incompetence, and the admittedly undersized Gambier Bay caught by surprise at close range by overwhelming Japanese assault. In all other cases, the advantage has squarely gone to aviation, with the fates of the former's fellow Brits Prince of Wales and Repulse demonstrating the vulnerability of actively evading capital ships - as opposed to the sitting ducks at Pearl Harbor - to air attack and the Japanese Yamato providing object lessons as to the impossibility of uncovered surface elements closing with a competent carrier task force. However, in a universe where the FTL has a lack of No Warping Zone, enemy battleships could bypass screening elements to "jump" into close quarters combat and shred carriers with Alpha Strikes, denying your side most of its strikecraft and thus offensive power, insofar as this is a universe where fighters have useful anti-capital firepower. In such a universe, it would only make sense to armor and upgun carriers to survive these sorts of lightning strikes, thus giving rise to the battlestar concept.
Perhaps the final point to remember is that, unlike the tried-and-true wet navies of today, the Space Navy is entirely uncharted territory. Since nothing of the sort has yet been attempted, much less proven, it's easier to devise hypothetical rules and ships to function within said rules than it is to work within the more rigid limitations of reality.
