Can the bags inside the cereal boxes be recycled?
Many cereal box liners are made from HDPE (#2 plastic) film. Rigid HDPE, commonly seen as things like milk jugs, is often accepted by curbside recycling programs. But plastic in film form (including bags) should not be added to your bin because it can jam up and damage recycling machinery. Instead, #2 plastic bags and other plastic film can be dropped off for recycling at one of thousands of retail locations. As with any kind of food packaging, make sure all traces of cereal residue are removed from the bag to avoid contamination.
Be aware that not all cereal bags are made of #2 plastic. If the bag tears like paper, or if you can’t find a plastic resin number on it, play it safe and either reuse the bag or trash it. There are many ways you can reuse cereal box liners around the house, including as a substitute for wax paper or to hold other objects such as papers and magazines.