Is it cheating when a man you have been living with for six years goes on single dating sites, ?

He goes on single dating sites, has exchanged email phone numbers and pictures. All of this is done when I'm not home. Some of the texting when on when I was in the other room. We separated for 5 mths. and now we are back together. He says he never cheated, just flirted. I say it's wrong, he doesn't think he did anything wrong.