The influence of dimensionality on the electronic properties of layered perovskite materials remains an outstanding issue. We address it here for Sr3Ir2O7, the bilayer compound of the iridate Srn+1IrnO3n+1 series. By angle-resolved photoemission spectroscopy we show that in this material the interlayer coupling is large and that the intercell coupling is, conversely, negligible. From a detailed mapping of the bilayer splitting, and from the intensity modulation of the bonding and antibonding bands with photon energy, we establish differences and similarities with the prominent case of the bilayer superconducting cuprates.