Composites of Immiscible Solids - Aluminum and Lead Example The $\ce{Al}$-$\ce{Pb}$ (aluminium-lead) phase diagram clearly depicts that when cooled from the liquid state, aluminium and lead are not miscible in the solid state, i.e. the crystal structure of only one of the components prevails while the other remains a liquid or does not interact in any way with the other in its own solidification process. 

What does this have to do - if anything - with the fact that a solid combination of $\ce{Al}$ and $\ce{Pb}$ is not classified as a composite?
You are correct that solid Al (fcc) and Pb (fcc) are (surprisingly for both being fcc) not miscible in each other (well, there is always some miscibility as driven by entropy). Heck, there is even an miscibility gap in the liquid phase as well. Al and Pb really don't like each other. 

So, as you cool the liquid from above 1418C (the top of the liquid miscibility gap), you will phase separate in the liquid phase. At the aluminum melting point, the aluminum will solidify, and the Pb will remain liquid. When the Pb melting temperature is reached, the Pb will solidify. The exact specifics of the solidification will depend on how it is done (the kinetics), not the thermodynamics. This means you can't predict the final micro-structure without  details of the process.

The final result will be solid Al and Pb, likely intermixed. It is not an alloy, but a two-phase mixture. I would not call it a composite as I would generally reserve that name for actual composite materials.