By far the best mattress for anyone suffering from allergies or mites is one made entirely of latex foam. Latex, being made up of millions of tiny air bubbles, allows natural transpiration, which prevents the development and spread of bacteria and other microorganisms.
There are other cheaper products, which nevertheless have good non-allergenic and anti-mite properties. When you decide to buy a new mattress, the important thing is to talk to the dealer, who can provide you with useful information and technical details