Differences between miscible and soluble
Your definition is basically correct, except using two liquids might provide for a clearer example than a solid and a liquid.  For example, diethyl ether is soluble in water to about 7% at $\mathrm{20^oC}$. This does not mean that diethyl ether is partially miscible in water, but that it it partially soluble. This Wikipedia article provides a good distinction for miscibility:  


  Miscibility is the property of substances to mix in all
  proportions (that is, to fully dissolve in each other at any
  concentration), forming a homogeneous solution.