How is it possible that non-US airlines are allowed to operate flights with their own aircraft in the US?
It's not (with traffic rights), and they don't. The short-haul Iberia and Air France from MIA
leave the United States to other countries.
International airlines can, and do, operate domestic segments in the US, but they cannot get traffic rights unless the passenger originated outside the US on the same flight. For example, El Al flies TLV
. A passenger cannot buy a ticket on the EWR
portion of the flight, but they can fly TLV
, stay in Newark for a few days, and then fly the EWR
A320 is Air France owned and operated. Iberia's A319s are as well. Iberia operates a full mini-hub operation in Miami, including a pilot base, FA
base, and maintence base.