My maternal great-grandmother, Angelina Benetti, is most likely related to your father born in Asiago. Apparently, the name Benetti is very common in that area. Here is her information:

Birth 13 Sep 1878 in Schio, Vicenza, Veneto, Italia
Death Abt. 1943 in Woonsocket, Providence, Rhode Island, United States

She was married first to Antonio Rubega and had 1 child, Alfredo Rubega. They immigrated to Paterson, New Jersey where Alfredo had a brother.
Antonio died around 1899 in Schio (they went back when he became ill and while Angelina was pregnant).
She returned to the US with her sister and mother. She very quickly married Eugenio Bellini, my great, great grandfather. They first lived in Allentown, PA with relatives (I think her brother or cousin), and my grandmother, Esther Bellini and Grand Uncle Mario Bellini were born. They then moved to Woonsocket, RI and in the 20s moved to a big farm right over the border in Blackstone, Worcester, Massachusetts.
Her father was Francesco Giovanni Benetti, who also came to the states with his wife Eliza Delmasetto Benetti