Mick Philpott, 55, and his wife Mairead, 31, appeared at Nottingham Crown Court following the blaze at the house on Victory Road in Allenton, Derby, on May 11.
Jade, 10, John, nine, Jack, seven, Jessie, six, and Jayden, five, all died in the fire, and a sixth sibling, Duwayne, 13, died of his injuries in Birmingham Children’s Hospital two days later.
Philpott, who wore a white sports vest top, stared at the floor while his wife, who wore a blue sweater, appeared tearful.
A member of the packed public gallery left the courtroom and shouted “disgrace” at the pair.
As the couple were remanded into custody, others in the gallery shouted “scum”.
No applications were made for bail and Judge Charles Haddon-Cave remanded them in custody. They will next appear at Nottingham Crown Court on June 18 for a preliminary hearing.
A crowd of around a dozen people shouted insults at security vans carrying the Philpotts.
The disturbance followed another at the couple’s first appearance at Southern Derbyshire Magistrates’ Court on Thursday when a man and woman were removed from the courtroom.