Interference lines on TV - how do I get rid of them?

Hi I'm getting pretty bad intereference lines on a TV I have.

This is the set up I have:
I have two coaxial cables coming into the house, one from a terrestrial aerial, and another from a Sky dish. The cable from the terrestrial aerial splits and goes into several rooms.

I only have Sky in one room and I want to feed the output from Sky back onto the terrestrial cable so I can view Sky in other rooms.

But the problem is I'm getting this interference when I do it (you can see the horizontal lines in the images).

Any ideas on how to get rid of it? I am using very ordinary coaxial cables from the sky box to the terrestrial cable's socket so could that be picking up interference?

Also: usually I keep both television "circuits" separate. When I plug the terrestrial cable into the sky box's input, it causes the same inteference on the sky output. So it only seems to happen when both circuits are connected. It happens putting the Sky signal onto the terrestrial circuit, and the terrestrial circuit onto the sky signal:)