Often it is useful to know what happens if you add substance A to substance B. Parameters describing important properties may be available, often it is interesting to know how well they mix. I will try to further clarify the terms miscibility and solubility based on my understanding of these concepts.
Miscibility is a binary property pertaining to two substances, commonly in liquid phase. Two liquids A and B are miscible iff: they form a homogenous distribution regardless of the amount difference between A and B. They are immiscible if this requirement is not met. We commonly talk about two liquids because all other phase interactions are either always miscible (gas-gas or molecular solid-solid interactions) or always immiscible (liquid non-liquid or solid-gas).
Solubility describes the ability/amount of A(any phase) to dissolve in B(liquid or gas). Dissolve means to homogeneously distribute itself. So nothing can dissolve in a solid (anything that disperses into a solid is a colloid) and if B is a gas only other gasses can dissolve in it. So water or ice can not dissolve into air(a gas) without boiling, e.g. humidity caused by evaporation is not actually homogeneous–without convection it tends to be higher near surfaces.
Describing solubility between two miscible substances is redundant. It can be said that miscible liquids have infinite or 100% solubility in each other—they are soluble in all proportions. By definition all gas-gas mixes are also miscible. Solids do not dissolve into other solids; yet powders can be mixed in all ratios so in theory all solid-solids could be said to be miscible if ground to fine molecular powders. An important conclusion is that a description of the parameter ‘solubility’ of A is only worthwhile iff: the solvent B is a liquid, and if A is liquid it is immiscible with B.
If A is a gas the pressure plays an important role in solubility. If it is a solid we should remember that a dissolved solid does not always have to break down into anions and cations.
When we think of immiscible liquids we typically imagine something like oil and water sitting separate in a glass bottle, the denser water below. But immiscible liquids need not completely separate. They can form colloids, suspensions or even solutions. E.g. part of A may still enter B and/or vice versa, how this fraction is distributed depends on the properties of A and B. Small amounts of water can actually dissolve in oil, and vice versa. Another common example of non-separated immiscible fluids is an emulsion.
On a final note, sometimes it is not easy to determine by eye if you have a colloid or a solution. In extreme cases it may be that a particle or the heterogeneity is too small to qualify as a colloid (sub-nano scale). So technically it is possible to have a heterogeneous solution, simply because chemistry has no other word for it.