Kenneth Browne and Melissa Browne appeared before Chief Magistrate Marcia Ayers-Caesar in the Port of Spain Magistrates Court today.
The accused were once married, but are now divorced.
Four other suspects have been released, including a 24-year-old man, named only as “Dole” who turned himself in for questioning last Wednesday night.
WPC Joseph was reported missing on Friday 10 March after she did not appear for work and relatives tried to contact her on her cell phone without success.
She was attached to the Morvant Police Station and was the mother of a 4-year-old girl.
Police had detained the 38-year-old male friend of the victim at the Besson Street Police Station in relation to her disappearance one day after she was reported missing.
The 28-year-old woman had been questioned by authorities last Thursday, after investigators learned she had had a falling out with the WPC before her disappearance.
Several searches were conducted both on land and at sea with a heavy police presence in Sea Lots since her disappearance.
Her body was eventually found in a bag, weighted down by bricks, by fishermen on Wednesday.
An autopsy conducted on her body, which was said to be badly decomposed, was inconclusive.
The case has been postponed to April 18.