Context. The annihilation of positrons in the Galaxy's interstellar medium produces characteristic gamma-rays with a line at 511 keV. This gamma-ray emission has been observed with the spectrometer SPI on ESA's INTEGRAL observatory, confirming a puzzling morphology with bright emission from an extended bulge-like region, while emission from the disk is faint. Most known or plausible sources of positrons are, however, believed to be distributed throughout the disk of the Milky Way. Aims. We aim to constrain characteristic spectral shapes for different spatial components in the disk and bulge using data with an exposure that has doubled since earlier reports. Methods. We exploit high-resolution gamma-ray spectroscopy with SPI on INTEGRAL based on a new instrumental background method and detailed multi-component sky model fitting. Results. We confirm the detection of the main extended components of characteristic annihilation gamma-ray signatures, altogether at 58σ significance in the 511 keV line. The total Galactic 511 keV line intensity amounts to (2.74 ± 0.25) × 10 −3 ph cm −2 s −1 for our assumed model of the spatial distribution. We derive spectra for the bulge and disk, and a central source modelled as pointlike and at the position of Sgr A*, and discuss spectral differences. The bulge (56σ) shows a 511 keV line intensity of (0.96 ± 0.07) × 10 −3 ph cm −2 s −1 together with ortho-positronium continuum equivalent to a positronium fraction of (1.080 ± 0.029). The twodimensional Gaussian that represents the disk emission (12σ) has an extent of 60 +10 −5 degrees in longitude and a rather large latitudinal extent of 10.5 +2.5 −1.5 degrees; the line intensity is (1.66 ± 0.35)×10 −3 ph cm −2 s −1 with a marginal detection of the annihilation continuum and an overall diffuse Galactic continuum of (5.85 ± 1.05) × 10 −5 ph cm −2 s −1 keV −1 at 511 keV. The disk shows no flux asymmetry between positive and negative longitudes, although spectral details differ. The flux ratio between bulge and disk is (0.58 ± 0.13). The central source (5σ) has an intensity of (0.80 ± 0.19) × 10 −4 ph cm −2 s −1 .