Actually, most of it was made of wood. The pilot's station is heavily armoured.
Only the rear fuselage and fin was made of wood - birch shpon, as the Soviets called it, laminated sheets, the wings and hori stab were light aluminium, while the fuselage and nose cowl panels was made of armoured steel. The aircraft was quite an engineering challenge for Ilyushin and the first prototype was a non-flying engineering mock-up with the intent of proving its structural elements, the issues with aligning the armour plating in sections with each other were considerable, particularly with misaligned fastening holes.
AB-1 (Aviatsiyonaya Bronya) armour plating was used, which was nickel/monel steel alloy, which had to be formed to shape in the manufacturing process before hardening took place, after which it was difficult to cut or shape, hence doing it while it was soft. The armoured body was known as the bronyekorpus, literally armoured body and was difficult to make, also because of the scarcity of alloying materials in the wartime Soviet Union, although that didn't stop them producing a shed ton of them. The nose armoured panels were 4mm around the front and 5 mm on the lower sides and underside, with a 7 mm slab behind the gunner. Rivets were 5 to 6 mm steel, which was difficult to form, requiring powerful guns - forming steel rivets take practise, it has to be done in one hit, unlike ali rivets that can be "touched" to finely shape the tail with the bucking bar. The weight of armoured panels on the Il-2 was around 700 kg and the top of the nose cowl was made from ali sheet.
These are pictures of Il-10s, which were not far removed from the Il-2 in structure, located in the derelict aircraft park of the China aviation museum, which at the time I took these photos was out of bounds to the public, even more so now as the perimeter fence has been fixed. In the Il-10 the underside nose cowl panel is over a centimetre in thickness. I got this pointed out to me whilst visiting the MLP in Cracow, the guide kindly opened it up for me.
The difference between the Il-2 and Il-10 being that the rear fuse and fin are made of metal. Note the massive plate behind the pilot's head.
The armoured cockpit section was hand rivetted as can be seen here, note the sheet ali structure making up the framework for the clear sections, the thickness of the foremost flat plate being gauged by the interior framework.
In this picture you can see the disposition of steel armour and aluminium.