Are they ‘with’ the mafia? 

No. This is a common headcanon/ misconception that I’ve noticed in the fandom.

The Italy Brothers don’t run the Mafia, nor do they work for
them. Instead, they’re often victimized by them.

Since mobsters are more of a problem in the Southern half of
the country, Romano’s respectively more affected by their activities. [x]

Ex: Romano is frequently coerced into doing favors for the Mafia
against his will. He complies because he’s terrified of them.

Nonetheless, Romano has proven to be capable of standing up
to them.

Ex: With Spain’s life hanging on the line due to an economic recession, Romano refuses to hand over the imports he intends to use in saving Spain’s
economy.

Typically, however, he’s seen as easy prey for the Mafia to
get him to do their bidding.

It’s only in the above circumstance where he becomes “stronger”
than usual. Put another way, Spain’s potential death kicked in Romano’s fight
or flight instinct.

How They’re Affected:

Both Italy brothers are frequently stolen from. While some
of this is from regular pickpocketers…

Ex: Veneziano has his car and wallet stolen. [x]

Ex: Romano is well-trained in guarding himself against being
pickpocketed. [x]

…the Mafia [and corrupt politicians] also steal from the
Italy brothers, albeit indirectly.

The personification’s income, as in how much money they have
available to them in their wallet, is dependent on how wealthy their country
is. If the government is corrupt and funds are being frauded/ embezzled, the personification
doesn’t receive as much money as they should.

Ex: Veneziano’s wallet runs thin as a result of corruption
in the Italian government, specifically in the South.

It’s not like they’re not aware of this corruption either,
because they are.

Ex: Veneziano comments on the corruption within Rome’s
municipal government and casts his vote for Virginia Elena Raggi, whose
campaign ran on combatting corruption. [x]

The problem is that because the nations have little
influence in how their government
runs, they don’t have the means or resources to tackle this corruption.