Assuming you're not talking about HD VOD, there should be no interaction between the video signal and your internet connection. Every (non-VOD) channel is present at all times on the coax, whether you're watching it or not. Your internet connection and your video are delivered over different wavelengths on the fiber and over different frequencies on the coax.
If you can demonstrate this happening, you should have VZ dispatch a tech. This certainly not something that should be happening.
