Husband continuously lies to me...

He's a really sweet guy and is helpful especially with our 2 month old but he lies to me all the time... I catch him in lies and he still tries to lie to me about it... He's a very good lier but now being together for so long I know when he lies to me... And what really bothers me is when he swares on our daughters life... I tried to talk to him about the lying last night and I told him that I wouldn't be mad if he would just tell me the truth and that it makes me really upset when he lies to me and I told him I know when he lies to me now... He said okay and that he wouldn't lie anymore but this morning he lied to me again.... Other than this lying he's a good guy. He only has one other fault and it's that he is a flirt and will flirt with any girl in his path and he says he doesn't realize he does it... He also got fired from one of his previous jobs for apparently having sex with a co-worker in a break room while we were together. He told me it wasn't true and that some people tried to get him fired by telling management that they caught him and the girl in the act and it never happened... But I'm not sure what to believe anymore... I love him and I love our daughter but I don't know what to do anymore.... He's loving and sweet and surprises me with gifts and all that but his lying is out of hand sometimes... All I want is honesty.

Edit*** He got fired from the job a year and a half ago before we had our daughter... Should I call his previous job he got fired from and ask if there was evidence?