In component-based software development approaches, components are considered as black boxes, communicating through required and provided interfaces which describe their visible behaviors. Each component interface is equipped with a suitable data model defining all the types occurring in the interface operations. The provided interfaces are checked to be compatible with the corresponding required interfaces, by the way of adapters. We propose a method to develop and verify these adapters when the interface data models are different, using the formal method B. The use of B assembling and refinement mechanisms eases the verification of the interoperability between interfaces and the correctness of the component assembly.