The idea of something being 'solid' is a property of our macro-world i.e. the big stuff larger than atoms and molecules. It's the repulsive effect between the outer electrons of each atom (like charges repel) that gives us this feeling of something being solid and impenetrable. When we look more microscopically, at the components of atoms, they become composed of fields with various properties that have no sense of substance we can associate in our macro-world; they are, in effect, materially empty space. If you look at it like this, space pervades continuously through all things. You aren't far wrong.