“And he told us how he had seen the angel standing in his house, and saying, “Send to Joppa, and fetch Simon, whose surname is Peter, who will speak to you words, by which you will be saved, you and all your house.”
He then explained how once they were in the house they had been told that the reason that Peter had been sent for was because of an angel who had told them to send for him, so that they might hear his words and be saved, along with their households. This confirmation of an angelic messenger, and therefore the clear piety of those involved, would ease the fears of those who were listening. Those who were most Jewish in their thinking would interpret ‘saved' as meaning becoming faithful adherents to Jewish Christianity, and would thus temporarily be satisfied.
‘Standing in his house.' If a holy angel was willing to enter Cornelius' house, then surely it was acceptable for a mere human.