Luigia had been previously married to Barberi.

Michele, age 34, traveled to Boston through Ellis Island on 27 May 1911, leaving his father Vincenzo in Tramonti di Sopra, joining his wife Luigia in Boston at ? 21 ..?. Street. (She may actually have been at 21 Walker Street in Concord, New Hampshire which is where they lived at the time of the 1910 Census.

1920 Census - Milford, Worcester County, MA - Same address as 1918 draft registration.
Their ages differ from other records. Marriage record says she is two years younger than he. 1910 Census has them both the same age, 26, which doesn’t agree with others.
Michele Cozzi 43 Italy
Wife Louisa Cozzi 49 Italy

No record found for them the US after 1920. Apparently no children; in the 1910 Census she shows as having had one child, no longer living (and possibly with her first husband); no children shown in 1920.