A quick Google search (to uberproaudio.com) shows that three of the four guitarists in these two bands largely use all-tube combo amps-Fender Twin Reverbs, Fender Supersonics, Fender Hot Rod DeVilles, Vox AC4TV, etc. Obviously, these bands use way less distortion that you're average metal band; it's more of an overdrive sound.
As for guitars, these guys mostly use hollowbodies with humbuckers. Some Les Paul types, some Teles. The notable exception is Hammond of The Strokes, who is known to use a single coil Strat as his main guitar.
Short Version: all tube overdriven combo amps and hollowbody guitars generally forms the basis of this type of guitar tone.
I can get a good approximation going with my Fender Blacktop Strat (dual humbuckers as opposed to single coils) through my Vox AC15VR (the valve reactors, which is a hybrid tube solid state amp; tube for tone, solid state for volume).
Speaking of Interpol tones, I've always wondered how to get Carlos D.'s bass tone, best exemplified in the intro to "Evil" on the Antics record. I know he uses a Jazz bass and plays with a pick, but somehow he avoids that gnarly, growling tone the Jazz basses are known for (see Geddy Lee, Jaco, etc.), and more resembles a P-bass in tone. This is my ideal indie rock bass tone: very warm, not a lot of attack, but very clear and not muddy at all. I currently play a Fender Blacktop Jazz (a Jazz/P hybrid-a Jazz body with dual P pickups) and I also play with a pick (generally), and I can't quite get the attack out of there (via amp EQ/instrument tone knob) without it turning into incomprehensible mud. Any ideas?
Melodic Black Metal, Band, Drums
Cold Blank Stare
Black Metal, Solo Project, Everything