Most likely your input signal is symmetric around ground.
It's a video signal, it's not going to be symmetric around ground!!!
This is what a video signal looks like
Is it a composite video signal? If so where is the DC level?
Most likely you will have to AC couple the video signal input. Then apply a black level clamp or a sync tip clamp. Then you can put it through the multiplexer. Finally AC couple the output with a video driver.
look at Composite video - Wikipedia