The way I always played Chinese jumprope was “In, out, side by side, on, in, out.”
In- jump with both legs inside of the ropes.
Out- jump out of the ropes.
Side by side- Straddle one side of the rope (with one leg on each side of it), then straddle the other side of the rope.
On- step on one side of the rope with each foot.
out-jump out to one side.

If you did it without messing up, then the rope gets higher, and so on.

I was ok at double dutch, I didn’t get to play much because most of the kids I knew didn’t play it. I was GREAT at turning the ropes, though, hehe…