  The Orion Nebula Cluster (ONC) hosts protoplanetary disks experiencing
external photoevaporation by the cluster's intense UV field. These ``proplyds"
are comprised of a disk surrounded by an ionization front. We present ALMA Band
3 (3.1 mm) continuum observations of 12 proplyds. Thermal emission from the
dust disks and free-free emission from the ionization fronts are both detected,
and the high-resolution (0.057") of the observations allows us to spatially
isolate these two components. The morphology is unique compared to images at
shorter (sub)millimeter wavelengths, which only detect the disks, and images at
longer centimeter wavelengths, which only detect the ionization fronts. The
disks are small ($r_d$ = 6.4--38 au), likely due to truncation by ongoing
photoevaporation. They have low spectral indices ($\alpha \lesssim 2.1$)
measured between Bands 7 and 3, suggesting the dust emission is optically
thick. They harbor tens of Earth masses of dust as computed from the millimeter
flux using the standard method, although their true masses may be larger due to
the high optical depth. We derive their photoevaporative mass-loss rates in two
ways: first, by invoking ionization equilibrium, and second using the
brightness of the free-free emission to compute the density of the outflow. We
find decent agreement between these measurements and $\dot M$ = 0.6--18.4
$\times$ 10$^{-7}$ $M_\odot$ yr$^{-1}$. The photoevaporation timescales are
generally shorter than the $\sim$1 Myr age of the ONC, underscoring the known
``proplyd lifetime problem." Disk masses that are underestimated due to being
optically thick remains one explanation to ease this discrepancy.
