  In a class of two-component Ginzburg-Landau models (TCGL) with a
U(1)$\times$U(1) symmetric potential, vortices with a condensate at their core
may have significantly lower energies than the Abrikosov-Nielsen-Olesen (ANO)
ones. On the example of liquid metallic hydrogen (LMH) above the critical
temperature for protons we show that the ANO vortices become unstable against
core-condensation, while condensate-core (CC) vortices are stable. For LMH the
ratio of the masses of the two types of condensates, $M=m_2/m_1$ is large, and
then as a consequence the energy per flux quantum of the vortices, $E_n/n$
becomes a non-monotonous function of the number of flux quanta, $n$. This leads
to yet another manifestation of neither type 1 nor type 2, (type 1.5)
superconductivity: superconducting and normal domains coexist while various
"giant" vortices form. We note that LMH provides a particularly clean example
of type 1.5 state as the interband coupling between electronic and protonic
Cooper-pairs is forbidden.
