My solution for this is to assign everyone their own binder. Anything that needs to be kept for that person such as kindergarden lists, mailers, forms for my son will go in his binder. Papers that need filing, receipts, bills, etc. go in my husband and my binder. I keep the binders easily accessible so I can access them anytime I need them.
When I go through the mail and school backpacks, I easily put everything away where they should be - the garbage, the bill pile, the bulletin board or a binder. I know where all the loose papers are and don't have to worry that someone will throw them away by accident. You can also color code them if you have a color code system in your family.
This works well for us, and if you have a loose paper problem it is an inexpensive way to keep them organized!