I've seen surprisingly few Jersey Giant crosses talked about. I assume it is factor of hatchery stock Jersey Giants not being particularly remarkable and Jersey Giants in general growing slowly.
I'm currently experimenting with a Jersey Giant rooster crossed over Delawares. I was cautiously optimistic that the chicks were sex-linked when they hatched, and they definitely appear to be now. A little more than half were black with a dot on their heads, the rest were solid black. There was some reddish/ruddiness to some, but not all, chicks. Distinctly different from purebred Black Jersey Giant chicks (tuxedo colored).
Parents. Well, "Jersey" is the sire to all of them. There are 10 different Delaware pullets that could be their dams. Jersey is exhibition stock. The Delaware pullets are hatchery stock - some are better looking than others. In this picture, he was about 10 months old and the pullets were about 7 months old.
Fresh out of the incubator. The light colored chicks are purebred White Jersey Giants
Suspected cockerels at about 1 week of age. Definitely some variation in chick down color around the faces.
Similarly aged Black Jersey Giant chicks (there are a couple mixes and Lavender Orpingtons in here as well), but the tuxedo chicks are all BJGs.
Here is a pullet and a cockerel from this hatch at about 8 weeks of age. The cockerels are all barred. The pullets are black with varying amounts of gold/red in their feathers.
I would expect similar results of a Black Jersey Giant rooster x Barred Rock hens. Barred Rock rooster over Black Jersey Giant hens should give you all barred chicks. I'd expect Black Jersey Giant rooster over Rhode Island Red hens to give you black chicks with varying levels of red leakage.