A device was thrown at the front door of their house on the Toomagh Road, Castlecaulfield, about 0500 GMT on Friday.
The children, aged from 16 years to 8 months, were asleep when the device was thrown at their front door, setting a hall curtain alight.
The couple managed to put out the flames.
They said they had no idea why they were targeted.
The woman of the house added: "If it had gone in through that window my children would have been burned. My kids were panic stricken."
Earlier, army bomb disposal experts made safe the remains of a nail bomb which had exploded in east Belfast.
No-one was injured in the blast at the corner of Bryson Street and the Newtownards Road, shortly after midnight on Thursday.
However, the blast damaged a block of flats occupied by the elderly.
The police said the attack was not thought to be sectarian.
David Ervine of the loyalist Progressive Unionist Party said there had been tensions between the two communities in the area.
He called on people to be vigilant and said whoever was behind the attack was trying to "tap into the sense of fear which exists in the area".
In a separate development, the police said a possible sectarian attack was prevented after a bag containing two pipes and gloves was found in Dungannon, also in Tyrone, on Thursday night.
An army patrol discovered the items on the Killyman Road, near Killymerron Park.
The Presbyterian Moderator, Dr Trevor Morrow, has condemned the wave of recent pipe bomb attacks as a ''moral outrage''.
He accused the pipe bombers of having a ''reign of terror'' and spoke of his disgust at the attacks.
"This is black and white. This is not just wrong this is evil.
"It seems to be perpetrated by a militant loyalist faction their motivations we are not sure, but we are concerned that out Roman Catholic neighbours understand that for this to be done in the name of Protestant is outrageous to us."
Mr Morrow made the comments after a number of attacks on Wednesday night and Thursday.
Meanwhile, the railway line near Newry in County Down remains closed due to a security alert.
The alert on the track at Killeavy started on Wednesday night following a bomb warning and then reports of an explosion.
However, the police said they had not yet established the source of the loud bang, due to the terrain and the lack of any accurate direction.
They are appealing for help from the local community.
They want anyone who saw anything suspicious to contact detectives at Newry.
As a result of the security alert, train services between Newry and Dundalk, in the Irish Republic, have been suspended for two days, and passengers are being bussed between the towns.