Aims. We investigate the atmospheric structure and fundamental properties of the red supergiant VY CMa. Methods. We obtained near-infrared spectro-interferometric observations of VY CMa with spectral resolutions of 35 and 1500 using the AMBER instrument at the VLTI. Results. The visibility data indicate the presence of molecular layers of water vapor and CO in the extended atmosphere with an asymmetric morphology. The uniform disk diameter in the water band around 2.0 mu m is increased by similar to 20\% compared to the near-continuum bandpass at 2.20-2.25 mu m, and in the CO band at 2.3-2.5 mu m it is increased by up to similar to 50\%. The closure phases indicate relatively small deviations from point symmetry close to the photospheric layer, and stronger deviations in the extended H2O and CO layers. Making use of the high spatial and spectral resolution, a near-continuum bandpass can be isolated from contamination by molecular and dusty layers, and the Rosseland-mean photospheric angular diameter is estimated to 11.3 +/- 0.3 mas based on a PHOENIX atmosphere model. Together with recent high-precision estimates of the distance and spectro-photometry, this estimate corresponds to a radius of 1420 +/- 120 R-circle dot and an effective temperature of 3490 +/- 90 K. Conclusions. VY CMa exhibits asymmetric, possibly clumpy, atmospheric layers of H2O and CO, which are not co-spatial, within a larger elongated dusty envelope. Our revised fundamental parameters put VY CMa close to the Hayashi limit of recent evolutionary tracks of initial mass 25 M-circle dot with rotation or 32 M-circle dot without rotation, shortly before evolving blueward in the HR-diagram.