No bail was immediately set for Sidney and Tammy Moorer, who were charged in the abduction of Heather Elvis, ABC News reported Monday.
They were charged last week with indecent exposure and obstructing justice, the Horry County sheriff's office said.
Elvis' car was found abandoned at a local boat landing after she disappeared Dec. 13.
"Her car was parked where it shouldn't be, she was nowhere to be found, it was locked and no one was answering her phone," said her father, Terry Elvis.
Sidney Moorer's phone number was found multiple times on the missing woman's cellphone, the father said.
Investigators believe Heather Elvis and Sidney Moorer may have had a romantic relationship.
Sidney Moorer's attorney claimed his client was innocent because he "has connection to, nor knowledge of" the events surrounding Heather Elvis' disappearance.
An attorney for Tammy Moorer said she did not know the missing woman.