George Allen, 37, and his five-year-old son, Geordie, are critically ill in hospital after the incident at Killowen Primary School in Lisburn on Tuesday.
Mr Allen's seven-year-old daughter, Georgia, is stable.
The vice-principal of the school resuscitated Mr Allen using a defibrillator.
Education Minister Peter Weir praised the staff's "swift response" to the "traumatic situation".
He said his "hopes and prayers" were with Mr Allen's family.
Although the school was closed on Wednesday, staff met with independent counsellors to prepare them for any questions the children might ask when they return.
Democratic Unionist Party councillor Jonathan Craig, who sits on the school's board of governors, said the vice-principal would need support after his efforts at the scene.
"I know that over the next 24 hours, the real impact of what has occurred will probably hit him.
"That's where we need specialist help to try and counsel and give guidance to him and the rest of the staff."
Mr Allen is being treated in the Ulster Hospital in Dundonald.
His children are at the Royal Belfast Hospital for Sick Children and are thought to have suffered burn injuries.
The education minister has commended staff at a County Antrim school for their actions after a father and his two children were hit by lightning.