Mass exchange and mass loss in close binaries can significantly affect their evolution, but a complete self-consistent theory of these processes is still to be developed. Processes such as radiative shielding due to a~hot-spot region, or a~hydrodynamical interaction of different parts of the gas stream have been studied previously. In order to test the respective predictions, it is necessary to carry out detailed observations of binaries undergoing the largescale mass exchange, especially for those that are in the rapid transfer phase. \bla is an archetype of such a system, having a long and rich observational history. Our goal for this first study is to quantitatively estimate the geometry and physical properties of the optically thick components, namely the Roche-lobe filling mass-losing star, and the accretion disk surrounding the mass-gaining star of \blae. A series of continuum visible and NIR spectro-interferometric observations by the NPOI, CHARA/MIRC and VEGA instruments covering the whole orbit of \bla acquired during a~two-week campaign in 2013 were complemented with \ubvr\ photometric observations acquired during a three-year monitoring of the system. We included NUV and FUV observations from OAO~A-2, IUE, and Voyager satellites.