In this paper, the sensitivity of Atmospheric and Oceanic Coupled Models (AOCMs) to the coupling method is investigated. We propose the adaptation of a Schwarz-like domain decomposition method to AOCMs. We show that the iterative process of the method ensures consistency of the coupled solution across the air-sea interface, contrarily to usual ad-hoc algorithmic approaches. The latter are equivalent to only one iteration of a Schwarz-like iterative method, which does not provide a converged state. It is generally assumed that the lack of consistency does not affect significantly the physical properties of the solution. The relevancy of this statement is first assessed in a simplified problem, then in the realistic application of a mesoscale atmospheric model (WRF) coupled with a regional oceanic model (ROMS) to simulate the genesis and propagation of tropical cyclone Erica. Sensitivity tests to the coupling method are carried out in an ensemble approach. We show that with a mathematically consistent coupling the spread of the ensemble is reduced, suggesting that there is room for further improvements in the formulation of AOCMs at a mathematical and numerical level.