I used to get a local ag paper that had DHIA records from all the area farms published in it - it would include numbers like herd average pounds of milk, protein %, fat%, etc, and also what kind of cows: Holstein, Jersey, or X (crosses, and/or mixed herds). (No other breeds anymore
) The H herds would generally have 2.9 to 3.1 protein, the Jerseys 3.6 to 3.8, and the crosses right in between, 3.3 to 3.4. Same thing for fat. So, averaged out, component-wise the kinds of milk do seem to fall right in between the two breeds' norms - won't be quite as rich as full Jersey, but still much richer than pure Holstein.
That said, if this Holstein/Jersey cross you have is from a very small farmer with a few cows, it might not average out to the same extent, and might be more one way or the other. Management also factors in, too, though. For instance, if the cows are lower-producing than say a standard conventional farm, their components will likely be higher (it's a inverse relation: when production goes up, component %s go down). Or, feeding more roughage and long fibers, together with ample energy, in the feed, increases butterfat % (protein %s tend to stay about the same, I think, more genetic based and less affected by management).
I think too that I'd take raw H/J cross milk over pasteurized Jersey milk, if that was what the choice came down to.