Detectives in Mid Ulster investigating incidents in the Killymaddy Hill area of Dungannon on Sunday night have made two arrests.
Detective Sergeant Robinson said: "Shortly after 9:05pm it was reported two males arrived at a house, and that one of them may have been armed with a knife.
"When police arrived at the address, it was reported a petrol bomb had been thrown at the property, and a garden bench had been used to ram the front door, breaking a pane of glass. It was reported a second petrol bomb was thrown into the house.
"None of the occupants in the house, which included a man and a woman and young child and a baby, were injured, however this must have been a terrifying ordeal for them. This was a reckless attack which could have had a devastating impact, resulting in serious injury or worse.
"Officers subsequently arrested a 15-year-old male on suspicion of arson with intent to endanger life, while a 34-year-old man was arrested on suspicion of offences, including possession of an offensive weapon in a public place. Both remain in custody at this time.
"We are working to establish a motive for what happened and would appeal to anyone who was in the area last night at around 9pm and saw what happened, or anyone who may have been in the area earlier in the evening and saw anything out of the ordinary, to call our detectives on 101, quoting reference number 1402 09/02/20."
Anyone with information can also call Crimestoppers, which is anonymous, on 0800 555 111.