Do Mormons believe that marriage is eternal? Do Mormons believe that marriage is eternal?
Not automatically, but Latter-Day Saints do believe that marriage, and the family unit that it forms the foundation of, can and should be a sacred, eternal covenant that lasts "for time and all eternity" rather than simply "till death do you part."  Like other things of this life that touch on eternity, an eternal marriage has to be set up under Priesthood authority.  This is done in a holy temple, in a ceremony known as a sealing, where the marriage is "sealed" upon them under the same authority that was given to Peter in the New Testament, that what he should bind on earth would be bound in heaven.

This can be done as part of a wedding ceremony, or at a later point if the couple was already married before coming to the temple.  In the latter case, it is also possible to bring any children of theirs into the same covenant, to be sealed to their parents as an eternal family.  (This is not necessary for children born after the parents are sealed in marriage; they are considered "born under the covenant".)

See LDS article on Marriage