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My guess is that the two would be reasonably non-polar, so they would likely mix, but it may take some mixing or shaking.The density of liquid helium is 125 grams per liter.The density of liquid hydrogen is 70 grams per liter.So, at least initially, the hydrogen would layer above the helium.
The reason I asked was because of the work of Kamerlingh Onnes. Especially as shown here;http://iopscience.iop.org/0953-8984/21/16/164222This is counter-intuitive as are the properties of helium as a Bose-Einstein Condensate when expressed as a superfluid.
the helium-rich vapour phase sank to the bottom, having become heavier than the hydrogen-rich liquid phase.
The solubility of helium in liquid hydrogen has been measured as a function of temperature and pressure. It was found the solubility varied from 0.59 mole % for T=26.8°K and 1.98 atm partial pressure of helium to 11.1 mole % for T=19.8°K and 7.0 atm partial pressure of helium.