  Energetically stable ``core-and-mantle'' configurations of trapped
two-component immiscible Bose-Einstein condensates are considered theoretically
within the coupled Gross-Pitaevskii equations. Non-stationary long-lived
''soft'' excitations (coherent structures), that consist of several quantum
vortex filaments penetrating the ``mantle'' from outside to inside and
vice-versa and demonstrate quite nontrivial dynamics, are observed numerically
for the first time. The ends of filaments can remain attached to the interface
between the ``mantle'' and the ``core'' if the latter is large enough while the
surface tension is not small. The shapes of such ``bubbles'' are strongly
affected by the vortices and sometimes are far from being spherical.
