Thank you for your interest, Arturo.
The woman who helped me with the Italian research, a woman here in the U.S., wrote a couple of letters to Vicenza, Henry's stated birthplace, with no result. She said that Henry was probably not born in Vicenza proper, that there were several - probably not the correct word - municipalities - within Vicenza; and, unless I knew exactly where in Vicenza he was born, it was unlikely that I would find out where. She also checked to see if he had registered for military service in Italy, but she did not find a record.
Someone else told me there were Petrin families in Switzerland and referred me to a Switzerland genealogical Web site, but I found it difficult to interpret.
At this point, I am assuming that the parents went from country to country in search of work.
Thanks, again.
Bonnie