The couple had earlier pleaded guilty to charges related to the posting of YouTube videos.
Royal Barnes, 23, was sentenced to five years and four months in prison after pleading guilty to three counts of disseminating a terrorist publication and one count of inciting murder.
His 22-year-old wife, Rebekah Dawson, was sentenced to 20 months after pleading guilty to one charge of distributing a terrorist publication.
Judge Brian Barker said the videos the couple posted were extremely offencive and showed total disregard for the slain soldier's family.