  Context. Betelgeuse is the closest red supergiant (RSG); therefore, it is
well suited for studying the complex processes in its atmosphere that lead to
the chemical enrichment of the interstellar medium. Aims. We intend to
investigate the shape and composition of the close molecular layer (also known
as the MOLsphere) that surrounds the star. This analysis is part of a wider
program that aims at understanding the dynamics of the circumstellar envelope
of Betelgeuse. Methods. On January and February 2011, Betelgeuse was observed
using the Astronomical Multi-BEam combineR (AMBER) instrument of the Very Large
Telescope Interferometer (VLTI) in the H and K bands. Using the medium spectral
resolution of the instrument (R $\sim$ 1500), we were able to investigate the
carbon monoxide band heads and the water-vapor bands. We used two different
approaches to analyse our data: a model fit in both the continuum and
absorption lines and then a fit with a Radiative HydroDynamics (RHD)
simulation. Results. Using the continuum data, we derive a uniform disk
diameter of $41.01 \pm 0.41$~mas, a power law type limb-darkened disk diameter
of $42.28 \pm 0.43$~mas and a limb-darkening exponent of $0.155 \pm 0.009$.
Within the absorption lines, using a single layer model, we obtain parameters
of the MOLsphere. Using a RHD simulation, we unveil the convection pattern in
the visibilities. Conclusions. We derived a new value of the angular diameter
of Betelgeuse in the K band continuum. Our observations in the absorption lines
are well reproduced by a molecular layer at 1.2 stellar radii containing both
CO and H$_2$O. The visibilities at higher spatial frequencies are matching a
convection pattern in a RHD simulation.
