You can say that or you can say I am watching telly and eating dinner.

Like you said: I´m eating while watching TV. Another example is a little bit different: 一边吃一边说: ... half chewing, half speaking.... (but at the same time).

while I was doing ***** I was also doing ****** I am doing **** at the same time I'm doing *****

Doing two things at the same time, Or, While I was eating I was watching TV. As Beth said