Do airplanes have any kind of fire insulation?
Yes, aircraft have fire-protection systems as well with many of the materials being of such a sort.

From boeing.com about the fire-resistant/fire-suppression systems on their aircraft. You can see that most of the aircraft is covered in these materials. Emphasis mine.


  Interior components of Boeing airplanes meet flammability requirements prescribed in Title 14 Code of Federal Regulations (CFR) Part 25. These components include:

- Interior ceiling.
- Interior sidewall panels.
- Partitions.
- Galley surfaces and structure.
- Exposed surfaces of stowed galley carts and standard galley containers.
- Large cabinets and cabin stowage compartments.
- Passenger seat material.

  
  For materials in areas not covered by the CFR requirements, Boeing design guidelines are used to identify additional flammability, smoke, and toxicity requirements.
  The standards for flammability of insulation blankets have improved over time. A recent requirement change calls for the enhancement of the fire-protective features of insulation blankets in the event of an in-flight or post-crash fire. The latest standard increases protection by minimizing the contribution of the insulation blankets to the propagation of a fire. Thermal/acoustic insulation installed behind cabin interior panels with the appropriate fire-resistant properties can delay the onset of fire into the cabin in the event of a crash (see fig. 1). The insulation blankets, along with the airplane skin, must be capable of resisting burn-through from a fuel-fed post-crash fire next to the bottom half of the fuselage for a minimum of four minutes to allow passengers to evacuate the airplane before burn-through can occur.


You can also find out much more in that webpage about the various active and passive fire-suppression systems in aircraft.

The FAA Regulation about these systems can be found here in PDF format.