  The PAMELA collaboration recently released the $e^+$ absolute spectrum
between 1 and 300 GeV in addition to the positron fraction and the $e^-$
spectrum previously measured in the same period. We use the newly developed
three-dimensional upgrade of the DRAGON package to model those data. This code
allows us to consider a realistic spiral arm source distribution in the Galaxy,
which impacts the high-energy shape of the propagated spectra. At low energy we
treat solar modulation with the HelioProp code and compare its results with
those obtained using the usual force-field approximation. We show that all
PAMELA data sets can be consistently, and accurately, described in terms of a
standard background on top of which a charge symmetric $e^+$ + $e^-$ extra
component with harder injection spectrum is added; this extra contribution is
peaked at about 1 - 10 TeV and may originate from a diffuse population of
sources located in the Galactic arms. For the first time, we compute the energy
required to sustain such a relevant positron flux in the Galaxy, finding that
it is naturally compatible with an astrophysical origin. We considered several
reference propagation setups; we find that models with a low (or null)
reacceleration - tuned against light nuclei data - nicely describe both PAMELA
leptonic and hadronic data with no need to introduce a low-energy break in the
proton and helium spectra, as it would be required for high reacceleration
models. We also compare our models with the preliminary $e^-$ and $e^+$
absolute spectra recently measured by AMS-02. We find that those data,
differently from what is inferred from the positron fraction alone, favor a
high energy cutoff (about 10 TeV) of the extra component if this is uniquely
generated in the Galactic arms. A lower cutoff may be allowed if a relevant
contribution from powerful $e^-$ + $e^+$ nearby accelerators is invoked.
