No, really. Bob Kane is credited for having created Two-Face after seeing this poster for the 1941 film version of DR. JEKYLL AND MR. HYDE, starring Spencer Tracy.
At least, that's the common belief. I wish I could find something more substantial to back it up, but after years of disillusionment and disagreement, I find it harder and harder to tell how much Kane actually came up with, and how much was actually Bill Finger (or, in the case of the Joker, Jerry Robinson).
But nevertheless, I think it's safe to say there's no doubt that the core visual of Two-Face came from that image: just flipped around, and colored green (funny to think that, by the late 80's, it would become standard for his scarred side to be purple). In fact, when Two-Face is first depicted, he's shown reading a copy of THE STRANGE CASE OF DR. JEKYLL AND MR. HYDE, a touch with is typically on-the-nose for the era, except for an important twist: this is a Jekyll and Hyde who exist simultaneously.
Of course, the actual makeup for Spencer Tracy in the film of JEKYLL was less grotesquely monstrous, particularly compared to the almost fanged simian effects work by the more famous Jekyll/Hyde, Fredric March. You can see a bit of his Hyde here for yourself in this clip, along with the radiant Ingrid Bergman, singing a song which may make you smack your heads and go "oh my god!" if you've happened to read Alan Moore's THE LEAGUE OF EXTRAORDINARY GENTLEMEN vol. 2:
Another fun fact learned via Wikipedia: before either the March or Tracy versions, NOSFERATU director F.W. Mernau did another unauthorized adaptation of a classic horror story, this time doing JEKYLL AND HYDE under the title DER JANUSKOPF (translated as "The Head of Janus" or "The Janus-Head").
It featured Bela Legosi in a minor role, with the lead(s) performed by silent film titan Conrad Veidt. To the comics community, Veidt is more well known for being the physical inspiration for the only greater Batman rogue than Two-Face himself.
Unfortunately, the film is considered lost, but that doesn't mean a copy won't be found someday, hidden away somewhere. Man, wouldn't THAT be prize worthy of Two-Face's attention?