This relationship goes back to the early 20th Century.

Between 1881 and 1922, over two million Russian Jews and four million Italians immigrated to the United States.^(1, 2) The newly-arrived Jewish and Italian immigrants spoke alien languages, i.e. Yiddish and Italian, and practiced alien religions, i.e. Judaism and Catholicism. Consequently, many Americans perceived these immigrants as outsiders. Their outsider status marginalized them in American society. Moreover, many immigrant children grew up in desperately impoverished neighborhoods. Detroit’s east side, for example—from which originated the Jewish Purple Gang—was infamous for its high rates of death and disease, for which its horrific infrastructure was partially to blame.^(3) Like so many poor, marginalized groups throughout American history, Jews and Italians alike turned to crime to achieve material wealth and influence.^(4)

By the early 20th Century, many Jews and Italians had become leading figures in the American underworld. While Jewish and Italian gangsters often fought each other, their interests just as often aligned. Many ended up cooperating, and became closely associated with each other. Here’s one example: In the 1920s, Jewish and Italian underworld bosses decided to join forces and create a loose criminal confederation that later became known as the National Crime Syndicate. The Syndicate formed a coalition gang comprised of both Jewish and Italian contract killers. The gang functioned as the assassination squad for both the Jewish Mob and the Italian Mafia. When the existence of this assassination squad became public knowledge, the American media labeled them as “Murder, Inc.”^(5)

Another example is the relationship between Meyer Lansky and Charles “Lucky” Luciano. Both men became feared crime bosses, both developed extensive racketeering empires, and both helped create the National Crime Syndicate. Both men were also close associates of each other.^(6) As associates, both men used each other’s contacts, which—as leading racketeers—necessarily included accountants and lawyers.

Their association with each other proved very close. In the late 1930s, Luciano was convicted of racketeering charges, and began serving a 30-50-year sentence. With the entry of the United States into World War II, however, the Department of the Navy had to contend not only with German submarines operating off the Atlantic coastline, but also with the possibility of German agents sabotaging waterfront docks all over the eastern seaboard. Knowing that the Italian Mafia—and specifically Luciano—held extensive influence over the Atlantic waterfronts, the Navy approached Luciano. The Navy requested Luciano’s cooperation in gaining intelligence through his waterfront contacts about enemy infiltration. Luciano agreed to cooperate in exchange for an end to his prison term, and deportation from the United States. The Navy also contacted Lansky, whom Luciano trusted enough to become his intermediary for both his waterfront contacts and Navy intelligence personnel.^(7)

So it was from very close relationships like this that the image of the Italian Mafia in league with Jewish gangsters and their associates developed in the public consciousness.

I can't comment as to whether this kind of relationship between Jewish and Italian mobsters exists or at one point existed in other countries. Except Argentina, I'm unaware of any other countries that historically had substantial Jewish and Italian immigrant populations, which at least in America served as a prerequisite for the emergence of this relationship.

Endnotes

1 Rockaway, Robert A. “The Notorious Purple Gang: Detroit's All-Jewish Prohibition Era Mob.” Shofar, vol. 20, no. 1, 2001, pp. 113–130, p. 115

2 Stella, Antonio, 1868-1927. “Some Aspects of Italian Immigration to the United States: Statistical Data And General Considerations Based Chiefly Upon the United States Censuses And Other Official Publications.” New York & London: G. P. Putnam's Sons, 1924, p. 13

3 Rockaway, Robert. “American Jews and Crime: An Annotated Bibliography.” American Studies International, vol. 38, no. 1, 2000, pp. 26–41, p. 114

4 Ibid. p. 113

5 Whalen, Robert Weldon. Murder, Inc., and the Moral Life: Gangsters and Gangbusters in La Guardias New York. Fordham University Press, 2016, p. 51

6 Kelly, Robert J. The Upperworld and the Underworld: Case Studies of Racketeering and Business Infiltrations in the United States. Kluwer Academic / Plenum, 1999, p. 107

7 Ibid. p. 107

Sources

Kelly, Robert J. The Upperworld and the Underworld: Case Studies of Racketeering and Business Infiltrations in the United States. Kluwer Academic / Plenum, 1999

Rockaway, Robert A. “American Jews and Crime: An Annotated Bibliography.” American Studies International, vol. 38, no. 1, 2000, pp. 26–41.

Rockaway, Robert A. “The Notorious Purple Gang: Detroit's All-Jewish Prohibition Era Mob.” Shofar, vol. 20, no. 1, 2001, pp. 113–130.

Stella, Antonio, 1868-1927. “Some Aspects of Italian Immigration to the United States: Statistical Data And General Considerations Based Chiefly Upon the United States Censuses And Other Official Publications.” New York & London: G. P. Putnam's Sons, 1924.

Whalen, Robert Weldon. Murder, Inc., and the Moral Life: Gangsters and Gangbusters in La Guardias New York. Fordham University Press, 2016.

Edit: wording, formatting