I think it's a mistake to say that Hitler's regime was fascist, because it wasn't. There are many key differences between fascism and Nazism.
The word "Fascism" (derived from the Latin
fasces) was a purely Italian phenomenon. A
fasces was a bundle of rods with a projecting axe blade, carried by a
lictor in ancient Rome as a symbol of a magistrate's power - i.e. telling everyone who even thought of breaking the law that he could use either the rod or the axe (i.e. punish criminals by either whipping or beheading). The
fasces was used as an emblem of authority in Fascist Italy.
Hitler's regime was Nazi (formally named
Nationalsozialismus, i.e. National Socialism). It is a political ideology rooted in the nineteenth-century German racialist (
völkisch) movement, emerging in the context of Germany's defeat in WW1, the counter-revolutionary movement,
and the rise of fascism in Italy.
There are several key differences between fascism and Nazism. The main difference is that Nazism is characterised by its extreme focus on the supposed superiority of the "Aryan race" and the use of this belief to justify genocide, whereas fascism (like that of Mussolini's Italy) prioritised the state and national prestige over racial purity.
Also, Nazism viewed the state as a tool for racial advancement (advancing and expanding the "master race" through policies like racial expansion and eugenics), while fascism viewed achieving state prestige and power as the ultimate goal.
In Nazi Germany, the racial ideology was central and all-consuming, leading to the Holocaust and other genocides. In Italy, Fascism did not have a central racial doctrine, though it later adopted antisemitic laws.
Finally, Nazism sought to unite the nation by eliminating class distinctions in favor of racial unity. But Fascism accepted and sought to preserve the class system, with class collaboration serving the state.
But has there ever been a fascist democracy? I think that's a contradiction in terms. The hallmark of Fascism, and the thing that made it worked, was strict authoritarianism, with power concentrated in private enterprise and a leader. One of the first things that Hitler did was abolish unions and collective bargaining, two of the things that constituted a check on the absolute power of corporations that was spreading in the US.
Fascism and democracy cannot sustainably coexist as core governing logics. Apparent coexistence is temporary, superficial, or a stage in democratic decay. Long-term stability requires either the preservation of democratic institutions that restrain fascist tendencies or the replacement of democracy by an authoritarian system.
Democracy is liberal, and gives rights and liberties to citizens and to unions. Fascism absolutely subordinates the individual citizen to state power and outlaws unions.
It's essentially the difference between the Second Athenian League and the Power of Sparta after the Peloponnese War, or the Delian League (under Athens's leadership) and the Persian Empire. It is impossible for them to coexist in the same place in a stable way.