Jeanne A. Moore, 28, and Dereke Moore, 27, both of Smyrna are locked up and facing conspiracy and abuse of corpse charges.
On Monday morning, staff at Bayhealth Medical Center called police after Moore came in and was bleeding.
The hospital workers told police Moore stated she had given birth to a baby Saturday, two days earlier. The baby was stillborn, the couple said.
Investigators say neither Jeanne or Dereke Moore explained why they didn't call 911 on Saturday, but both apparently admitted they placed the baby in the trash bag together before Dereke allegedly place the infant in the dumpster.
Police recovered the baby's body and an autopsy is going to be conducted by the Delaware State Medical Examiners Office.
The couple faces up to two years in prison.