Not literally at the same time, but if your TV is new enough to support a dish input, then you can watch the Freesat channels. Connect a terrestrial aerial to the aerial port, and you can watch freeview channels. (the names of the providers are country dependent!) And the 'over air' digital channels should not need re-installing every time.
Kenton82s correct answer is UK oriented.
If you are in the US this might make more sense since we don't have any freesat channels.
You DISH sat box connects to an HDMI input so you select that input when you want to watch sat channels.
You select Antenna when you want to watch over the air TV.
You don't have to scan for channels every time,