A number of recent experiments on high quality samples of YBa2Cu3O7-δ (Y123) have indicated that the superconducting energy gap in this material is highly anisotropic. This has prompted us to investigate the possibility that Cooper pairs in layered copper-oxide are formed by electrons in different CuO2 layers. In this paper we report our findings on the physical consequences of interlayer pairing in materials with one, two and three conducting layers per unit cell, and the competition between intralayer and interlayer pairing mechanisms. One important result of our investigation is that, as required by time reversal invariance, the order parameters are associated with bands, not with layers as assumed in many recent publications on similar models. The two-layer model is particularly interesting because it gives a good account of the properties of the gap function of Y123.