  Existence of thermodynamically stable composite vortices in a two-component
superconductor may form distinctive vortex patterns, and may lead to type-1.5
superconductivity. Here we study the surface energy of the two-component
superconductor and show that the sign of surface energy is determined not only
by the Ginzburg-Landau parameters $\kappa_i (i=1,2)$ of two superconducting
components, but also by a temperature independent parameter $\kappa_\xi $,
which is defined as the ratio of the coherence lengths of two components. Since
the negative surface energy conduces to the invasion of thermodynamically
stable composite vortices into a superconductor, the criterions for stability
of composite vortex are these three independent dimensionless parameters. We
find that there can exist thermodynamically stable composite vortex in a
type-1+type-2 or type-2+type-2 material. We also predict that unusual vortex
patterns like those observed in $MgB_2$ (V. Moshchalkov et al, Phys. Rev.
Lett., 102, 117001 (2009)) can occur in some type-2+type-2 superconductors.
