The snack food maker is suing, alleging the packaging for Aldi’s store-brand cookies and crackers “blatantly copies” Mondelez products like Chips Ahoy, Wheat Thins and Oreos.

The lawsuit claims Aldi’s peanut butter creme-filled cookies, chocolate chip cookies and Thin Wheat crackers have packaging similar to Nutter Butter, Chips Ahoy and Wheat Thins, among other ...