The light distribution in the inner few kiloparsecs of the Milky Way is recovered non-parametrically from a dust-corrected near-infrared COBE/DIRBE surface brightness map of the inner Galaxy. The best fits to the photometry are obtained when the Sun is assumed to lie $\sim14\pm4\pc$ below the plane. The recovered density distributions clearly show an elongated three-dimensional bulge set in a highly non-axisymmetric disk. In the favoured models, the bulge has axis ratios $1{:}0.6{:}0.4$ and semi-major axis length $\sim2\kpc$. Its nearer long axis lies in the first quadrant. The bulge is surrounded by an elliptical disk that extends to $\sim2\kpc$ on the minor axis and $\sim3.5\kpc$ on the major axis. In all models there is a local density minimum $\sim2.2\kpc$ down the minor axis. The subsequent maximum $\sim3\kpc$ down the minor axis (corresponding to $l\simeq-22��$ and $l\simeq 17��$) may be associated with the Lagrange point L$_4$. From this identification and the length of the bulge-bar, we infer a pattern speed $��_b\simeq 60-70\kms\kpc^{-1}$ for the bar. Experiments in which pseudo-data derived from models with spiral structure were deprojected under the assumption that the Galaxy is either eight-fold or four-fold symmetric, indicate that the highly non-axisymmetric disks recovered from the COBE data could reflect spiral structure within the Milky Way if that structure involves density contrasts greater than $\gta 3$ at NIR wavelengths. These experiments indicate that the angle $��_0$ between the Sun--centre line and a major axis of the bulge lies near $20��$.

11 pages, submitted to MNRAS. ps-file including 15 figures. Also available at http://www.astro.unibas.ch/~gerhard/papers/cobe.ps.gz