Is it permissible for my husband to dispose of two movie tickets he won for his good performance at work, or to give them to a non-Muslim friend, knowing that we do not watch movies?

If the films contain unlawful elements such as the appearance of unveiled women, music, and alcoholic beverages, then it is not permissible to watch them, nor is it permissible to assist in their viewing, even if the viewer is a disbeliever. Your husband must destroy the two tickets or endeavor to return them to the company. This is the clear ruling concerning any unlawful item that comes into the possession of a Muslim if it cannot be utilized in a permissible way. Let your husband seek reward from his Lord, the Almighty, for what he will do.