In Under the Bridge by Red Hot Chili Peppers, the introduction alternates between D and F# chords, with an E in between as a passing chord in some cases. There is also a g# passing note played over the D chord, and together with the g# in the E chord, it gives the introduction a Lydian feel.
But how would you interpret the F# chord harmonically? I can't explain it in terms of modes, because in terms of scale degrees the 5th of the I chord is the 3rd of the III chord, so the I and III major chords cannot belong to the same scale/mode. I can't explain it in terms of a modal import either (no mode sharpens the dominant note).
Of course you could just say that the F# is an altered III chord and be done with it, but I don't find that satisfying because that argument can be used for literally anything. So I'm wondering if there's a more satisfying harmonic explanation, especially as this progression actually sounds pleasing and not at all 'random'.
PS: I come from a classical music background and I'm new to thinking in modes, so please forgive me if the question is stupid.