Rival factions of loyalist and nationalist youths threw petrol bombs as they clashed in a series of incidents in the Castlereagh Street, Mountpottinger Road, Woodstock Link and Albertbridge Road areas.
Police said the violence started when two rival factions fought in the Castlereagh Street area shortly before 10pm.
Officers were deployed to the area and youths dispersed quickly before a petrol bomb was thrown towards a property on the Mountpottinger Road.
Police said they recovered the remnants of the device for forensic examination and seized two other petrol bombs.
At around 11.30pm police said youths gathered at Woodstock Link where missiles were thrown.
The front window of a house on the Albertbridge Road was also smashed during the trouble.
Senior police described the attack on the house, which "terrified" the family, as serious.
Clare O'Donnell said her children, aged two and eight, were playing in the front room of the house when snooker balls were thrown at their windows.
She said they were forced to hide in an upstairs bedroom while the disturbance took place.
The 28-year-old told UTV it was lucky her children were not scarred for life after her living room window was put through.
I don't know why the same rival groups of people - on both sides - are allowed to get together and wreck people's lives.
She said: "It was men who came into my garden shouting 'UVF'. I don't know why or what they thought they would achieve, but they left me and my children terrified.
"It was horrendous, the windows are double glazed and so only the one of them was smashed through.
"But now were are having to sit with the light on all day because it is so dark in the house with the windows all boarded up and the children are asking why this has happened."
Police said there had been a recent spate of minor trouble over previous nights and Saturday's events were an escalation.
Ms O’Donnell added: "Boys come out to start the trouble and older men come out to finish it off.
"This has been going on for some time and the police know where the trouble is going to happen, but nothing is done.
"It can't be allowed to go on; someone has to put a stop to it. Everyone should be safe in their own home."
Following a period of relative calm at the interface there has been an escalation of disorder over the last few nights, largely involving groups of young people throwing missiles. This culminated in petrol bombs being thrown from both factions on Saturday night.
Superintendent Mark McEwan
Police said there were around 20 youths on each side, aged in their late teens to early 20s and divided along sectarian lines.
Superintendent Mark McEwan said: "At this stage there is nothing to say this was orchestrated by any group but any orchestration would be through social media.
"This was followed by a serious attack on a house on the Albertbridge Road which involved golf and snooker balls being thrown at the property breaking several windows and terrifying the occupants, who included children.
"We had resources at the scene and working with community representatives we were able to deal with the disorder."
He added: "We will have a proactive policing operation in place because we are taking this seriously and I would appeal for anyone with information to come forward.
"I would appeal to parents to know where their children are at nights.
"I would also appeal to those young people who may be involved."
Police say 48 people have been arrested at the interface since April.