  Astrometric measurements of microlensing events can in principle determine
both the "parallax" \tilde r_E and the "proper motion" \mu of an individual
event which (combined with the Einstein time scale t_E) in turn yield the mass,
distance, and transverse velocity of the lens. We show, however, that the
parallax measurements are generically several orders of magnitude less precise
than the proper-motion measurements. Fortunately, astrometric measurements by
the Space Interferometry Mission (SIM) are simultaneously **photometric**
measurements, and since SIM will be in solar orbit, these allow SIM to be used
as a classical (photometric) parallax satellite. We show that SIM photometric
parallaxes are of comparable precision to its astrometric proper-motion
measurements. For I=15 bulge stars, complete solutions with about 5% accuracy
in mass, distance, and transverse velocity can be obtained from about 5 hours
of observation, 100 to 10,000 times shorter than would be required for a purely
astrometric solution of similar precision. Thus, it should be possible to
directly measure the mass functions of both the bulge and the inner disk
(including both dark and luminous objects) with only a few hundred hours of SIM
observations.
