What is the moho discontinuity state of matter?
The Mohorovicic Discontinuity is a discontinuity in the composition of solid rock, but it is indeed solid on both sides.
The "Moho", as it is often called for brevity, is the boundary between the crust and the mantle. While the mantle has liquid further down, it's solid at the top just like the crust -- but with a different mineral composition.
We detect this discontinuity in the solid rock from seismic wave measurements, which show the waves being reflected and refracted by the discontinuity. That is how Andrija Mohorovicic discovered it in 1909.