  We study the boundary states of the archetypal three-dimensional topological
order, i.e. the three-dimensional $\mathbb{Z}_2$ toric code. There are three
distinct elementary types of boundary states that we will consider in this
work. In the phase diagram that includes the three elementary boundaries there
may exist a multi-critical point, which is captured by the so-called deconfined
quantum critical point (DQCP) with an "easy-axis" anisotropy. Moreover, there
is an emergent $\mathbb{Z}_{2,\text{d}}$ symmetry that swaps two of the
boundary types, and it becomes part of the global symmetry of the DQCP. The
emergent $\mathbb{Z}_{2,\text{d}}$ symmetry on the boundary is originated from
a type of surface defect in the bulk. We further find a gapped boundary with a
surface topological order that is invariant under the emergent symmetry.
