Context: Over the last decade a series of results have lent support to the hypothesis of the existence of a long thin bar in the Milky Way with a half-length of 4.5 kpc and a position angle of around 45°. This is apparently a very different structure from the triaxial bulge of the Galaxy. Aims: In this paper, we analyse the stellar distribution in the inner 4 kpc of the Galaxy to see if there is clear evidence for two triaxial or barlike structures, or whether there is only one. Methods: By using the red-clump population as a tracer of the structure of the inner Galaxy we determine the apparent morphology of the inner Galaxy. Star counts from 2MASS are used to provide additional support for this analysis. Results: We show that there are two very different large-scale triaxial structures coexisting in the inner Galaxy: a long thin stellar bar constrained to the Galactic plane (|b|<2°) with a position angle of 43.0 ° ± 1.8 °, and a distinct triaxial bulge that extends to at least |b|≤7.5° with a position angle of 12.6 ° ± 3.2 °. The scale height of the bar source distribution is around 100 pc, whereas for the bulge the value of this parameter is five times larger.