To be specific, what I mean is: is the following situation possible? At given temperature T, there are two substances, X and Y, such that pure X is a solid, pure Y is a liquid, and X and Y mix to form a single phase in all proportions.
The closest I could find was this phase diagram for silver and gold (two very similar metals, I suppose): http://www.crct.polymtl.ca/fact/phase_diagram.php?file=Ag-Au.jpg&dir=SGTE
But it looks like there is still a narrow region in which there are two phases.
It's not necessarily a strict definition of a single intermingling of phases, however the closest thing I can think of corresponding to this in reality would be interstitial metal hydrides.
These materials are being investigated as hydrogen storage materials, so essentially the hydrogen molecules interact with the metal to form hydrides, "$\ce{H-}$", which recombine under different conditions to reform $\ce{H2}$ as required. A review of this technique is given here.
It would be interesting, to answer your question more directly, if liquid hydrogen could be used instead of hydrogen gas (this requires temperatures of <33K). I imagine this process would give exactly the same result, albeit would happen more slowly than the gas phase.
