Integrating practices and methods of Interaction Design and Usability into Software Engineering processes has posed some challenges. In this paper we extend a SE process to enable its instantiation as user centered in order to improve the usability level reachable by the final system. Also, we suggest a kind of a road map that enables software organizations to instantiate cumulative versions of this process to grow in their capability regarding the usability practices. The paper is organized in two parts. First, we describe de open source version of the Unified Process (OpenUP) and the ISO Usability Maturity Model (UMM-ISO) and present the results of an assessment made on the first to determine its conformity with the latter. In the second part we present an extension to OpenUP to fill the gaps discovered and report the highlights of an implementation of these contributions in a real project and the lessons learned.