  We provide a detailed description of our previously proposed scheme for
topological interface engineering with constructed defects and textures
perforating across coherent interfaces between different broken symmetries [M.
O. Borgh and J. Ruostekoski, Phys. Rev. Lett. 109, 015302 (2012)]. We consider
a spin-1 Bose-Einstein condensate, in which polar and ferromagnetic phases are
prepared in spatially separated regions. We show that a stable coherent
interface is established between the two phases, allowing defects of different
topology to connect continuously across the boundary. We provide analytic
constructions of interface-crossing defect solutions that could be
experimentally phase-imprinted using existing technology. By numerically
minimizing the energy, we calculate the core structures of interface-crossing
defect configurations. We demonstrate nontrivial core deformations to
considerably more complex structures, such as the formation of an arch-shaped
half-quantum line defect, an Alice arch, at the interface, with the topological
charge of a point defect, whose emergence may be understood by the "hairy ball"
theorem. Another example of an energetically stable object is the connection of
a coreless vortex to a pair of half-quantum vortices. We show that rotation
leads to spontaneous nucleation of defects in which a coreless vortex
continuously transforms to a half-quantum vortex across the interface.
