Other than WWII films, I can't think of any Hollywood that actively promotes NATO in anything other than a joke. Even the more common cop shows, once an investigation goes international and INTERPOL has to be brought it, it's always a big sigh as if "oh boy, here's where the wheels fall off the bus" as the member agencies that make up INTERPOL are definitely looked down upon.

The flip side of this is watching European shows, and they all feel like US law enforcement is just a bunch of gung ho gun toting cowboys. Neither view is entirely accurate, nor are they inaccurate as they are just stereotypes

I don't think it was Hollywood per se but The Day After did.

I've heard that a us tv show about marines or whatever used to include European, Mexican and south American special forces as allies regularly, to add realism in conflict they're not alone in.