  We present a detailed analysis of the the structure of the Local Group
flocculent spiral galaxy M33, as measured using the Panchromatic Hubble
Andromeda Treasury Triangulum Extended Region (PHATTER) survey. Leveraging the
multiwavelength coverage of PHATTER, we find that the oldest populations are
dominated by a smooth exponential disk with two distinct spiral arms and a
classical central bar $-$ completely distinct from what is seen in broadband
optical imaging, and the first-ever confirmation of a bar in M33. We estimate a
bar extent of $\sim$1 kpc. The two spiral arms are asymmetric in orientation
and strength, and likely represent the innermost impact of the recent tidal
interaction responsible for M33's warp at larger scales. The flocculent
multi-armed morphology for which M33 is known is only visible in the young
upper main sequence population, which closely tracks the morphology of the ISM.
We investigate the stability of M33's disk, finding $Q{\sim}1$ over the
majority of the disk. We fit multiple components to the old stellar density
distribution and find that, when considering recent stellar kinematics, M33's
bulk structure favors the inclusion of an accreted halo component, modeled as a
broken power-law. The best-fit halo model has an outer power-law index of $-$3
and accurately describes observational evidence of M33's stellar halo from both
resolved stellar spectroscopy in the disk and its stellar populations at large
radius. Integrating this profile yields a total halo stellar mass of
${\sim}5{\times}10^8\ M_{\odot}$, giving a total stellar halo mass fraction of
16%, most of which resides in the innermost 2.5 kpc.
