First I'm going to assume there is a good reason why Airships have become dominant, a reason that is not relevant to the airships.
People tend to think of Airships as slow and made of explodium. Yet Airships are actually incredibly resiliant and hard to spot on Radar. The envelope lets most radar beams through or absorbs it and there's very little heat except at the engines, which are relatively low-power compared to any modern aircraft. On top of that things like missiles, rockets and shells will simply pass through the envelope and not detonate. The gas inside is not pressurised so it won't instantly escape the envelope but use slow diffusion, and hydrogen (if helium isn't used) needs a certain mixture of oxygen and hydrogen before it can ignite. In WW1 entire drums of incendiary ammunition could be spend without causing a fire, because enough gas had to leak out and mix with the air before a fire could be started.
Modern techniques can increase safety. For example by surrounding hydrogen gas cells with helium gas cells to have a barrier that reduces the chance of a fire, on top of compartimentalizing which area's catch fire. Compartimentalizing into different cells is also immensely useful. With WWI (!) era technology they had build airships that could lose more than 25% of their gas and still limp back home. Even when the vulnerable Gondola's were shot off some managed to land (1).
Airship speed and size:
Most people think airships are slow, if only because most movies show them slowly moving around. Yet airships build with WWI and WWII technologies could reach speeds of up to 130km/h. Modern prototypes like the Airlander (2) can go up to 150km/h. For an aircraft that is slow, for an aerial vehicle larger than the Hindenburg and reaching the size of the largest modern aircraft carriers that is incredibly fast. The capacity of the Hindenburg was 46.000 pounds (9,5 tons) of cargo, a quarter of the capacity that your airship has left meaning the size of your airships have to be incredibly huge. Although modern materials and design would save a lot of weight, as proven by the Airlander which can carry 10 tons at 1/3rd of the length of the Hindenburg. Caveat there is that the airlander is designed as a modern cargoship, rather than combat vehicle.
The typical idea of an airship people have is a giant balloon with a vulnerable Gondola below. Those are non-ridgid airships (blimps), and are just one type of airship. These use the gas cells to keep their shape and require a separate compartment for the Gondola. However ridgid airships (the Zeppelin) and semi-ridgids can build the gas cells in almost any configuration and shape imagineable. The hindenburg for example had most of it's walkways and maintenance inside the envelope of the airship with gas-cells surrounding those. Design wise ridgid and semi-ridgid airships can be build in many more shapes, such as a wing-design that allows airships to fly using lift from the wing, meaning there is no need for enough gas to keep the airship airborne and let it float down if speed is lost.
One of the key features of Airships is that they don't go down with a single hit. Rather than make it easier for rockets, missiles and shells to explode upon contact I would focus the armor on limiting shrapnel damage. The cells would be compartimentalized between things like Kevlar fabric or equivalents to catch fragment and reduce tearing, but not enough kevlar to snag shells and missiles causing them to explode. Vital area's would be protected by hiding them inside the envelope and creating titanium tubs around them, similar to how planes like the A10 have a titanium tub around the cockpit. The logical step would be to place these types of armor in places where an explosion will move through the least amount of cells should it hit.
Other protections would include trying to make it hard to judge exactly where the envelope begins and ends in the hopes of making modern missiles explode prematurely, too late or above/below the actual airship. Airships are relatively cheap and would be unlikely to go down by a single modern anti-air missile, which can cost anywhere from 100.000 to several million, with a higher chance of detection and a low potential of being shot down prematurely due to CIWS mounted on the airship (if not Block type missiles). To down airships it is likely that new types of missile will be developed to be cheaper when trying to down an airship.
You could even consider airships that are simply designed to attract enemy fire. They carry minimal weaponry and are as cheap as possible, they are made to look like their more dangerous brethren and focus on staying in one piece while taking hits, eventually just landing the ship or bailing using alternative means.
Unless you use a Blimp design your ship will have an internal structure for strength that holds much of the gas cells together. This internal structure can at minimum handle anything modern aircraft can as it has less restrictions on weight. This means that it could carry and fire at least a 105mm Howitzer like the AC-130 Gunship, as long as the recoil is transferred directly to the internal support structure of the ship.
Combat techniques in Airship vs Airship combat:
There are 3 options in this type of combat:
- Destroy the internal frame, causing the airship to destabilize and crash.
- Destroy enough vital components like the bridge(s). Airships are resilliant by having many redundancies so having multiple vital parts to stay airborne is likely.
- Destroy enough gas cells to cause the airship to crash. Although it's likely the airship would descent first and need more gas cells broken before an actual crash occurs.
Large shells like a 105 gun could be used to punch through armor and destroy vital parts, however the (relatively) limited range would be an issue. Similarly smaller shells like a 30 to 40mm auto-canon could be used to increase the amount of gas-cells that are punctured. Most of these auto-canons when used for AA duty will detonate when they reach the target's range, spraying shrapnel to maximise hit-chances and destruction of an aircraft. This would likely also be used to maximise gas cell destruction.
Rockets could extend the range, but with long-range combat you need to properly detect the opposing airship, which apparently isn't as easy as with regular aircraft. It could be useful for stand-off attacks but without a proper range most of these rockets, if they even hit, would simply pass through the envelope and deal relatively minor damage compared to the size of the entire airship.
Missiles would be best for long-range combat, using similar properties as the shells by detonating and launching schrapnel into the aircraft to maximise hit chances and downing the aircraft. The question is what you choose to use. High-velocity missiles with optical sensors are likely a guaranteed hit if you have an approximate location of your target, but they are very expensive and you will likely need a lot of them to actually down a single one. Using cheaper radar or heat seaking technologies might not be good enough to detect and detonate properly. You could focus your story on the ECM side, where airships have so much spoofing and decoys to make downing them with missiles hard and force combat at much closer ranges with other weapons if you want that WW2 naval combat idea that we've already seen in space opera's.