That is a very good question! Only one person will be able to watch the Slingbox at a time. If you wanted to not interrupt the family viewing then you will need to have a dual tuner cable box. One tuner to have the family watch and the second one could be attached to the Slingbox access.
It can also be done if you have two routers.
Here is a link for you to check out: Help setting up Internet Viewing when you have multiple routers.
Hope this helps with your issue!
Have a great day!
Sling Moderation Team
The answer to your question may also depend on the way that the signal from your service provider currently gets to your TV. If you have a cable box delivering the signal to the TV, then you will need a second, separate cable box to deliver that same signal to your Slingbox Pro HD. The Slingbox Pro HD does have a built-in tuner, but this works only for those cable signals that come directly from the wall to the SB, without going through an intermediate cable box. In the USA, cable TV service providers are required by FCC regulation to provide a limited number of channels directly from the wall without going through a cable box. These channels typically include the local affiliates of the 3(4) major networks, plus local community public service channels, plus possibly a few others. If you are watching all of your channels via this no-cable-box-required method, then a simple two-way splitter attached to the wall wire, with one wire from the splitter going to the TV and the other wire from the splitter going to the SB-HD would allow you to sling one channel while the people watching the TV can be on another channel.