  We consider the vortex matter in a three-dimensional two-component
superconductor with individually conserved condensates with different bare
phase stiffnesses in a finite magnetic field, such as the projected
superconducting state of liquid metallic hydrogen. The ground state is an
Abrikosov lattice of {\it composite}, i.e. co-centered, vortices in both order
parameters. We investigate quantitatively two novel phase transitions when
temperature is increased at fixed magnetic field. {\it i)} A ``vortex
sub-lattice melting" phase transition where vortices in the field with lowest
phase stiffness ("light vortices") loose co-centricity with the vortices with
large phase stiffness ("heavy vortices"), thus entering a liquid state.
Remarkably, the structure factor of the light vortex sub-lattice vanishes {\it
continuously}. This novel transition, which has no counterpart in one-component
superconductors, is shown to be in the \xy universality class. Across this
transition, the lattice of heavy vortices {\it remains intact}.
