How does solutions of two liquids work?
It has already been pointed out that your text is incorrect. Saccharose (commonly known as sugar) is not an ionic compound yet it dissolves very well in water. It is not alone although I am too lazy to think up a non-carbohydrate example.
I’ll also point out that ionic compounds exist that are insoluble or poorly soluble in water, although some may rightly argue that their bonds tend to be more covalent than ionic.
As for two different liquids mixed together, the answer is: You can’t say a priori. (Or, in a highly logical reading of your question: no, the result will not always be a solution.) Many polar liquids will form a solution with many other polar liquids but in some cases the pairing will not. Conversely, a polar liquid such as ethyl acetate or acetone can form a solution with a practically unpolar liquid such as hexane.