2 of the 3 girls are not biologically his and he knew this at the time of birth and now that he has a new girlfriend he does not want the responsibility anymore. We are currently going through a divorce and he is going to petition to have his name taken off the birth certificates.

He probably can't.

If, as you say, he knew the children were not his, he should have objected then. Now is too late, I suspect, for him to overcome the presumption that children born in wedlock are those of the husband.

What state are you in?

2 of the 3 girls are not biologically his and he knew this at the time of birth and now that he has a new girlfriend he does not want the responsibility anymore. we are currently going through a divorce and he is going to petition to have his name taken off the birth certificates.

Depends on your location and the age of the children. States have varying laws regarding SOL on paternity cases.

Were you married at the time of the children's births or did he sign a paternity acknowledgment, accepting legal responsibility for the children? Depending on the circumstances, he can always claim you lied to him and he was unaware that they were not his biological children.

We are in Ohio and we were married at the time of birth the children are 8, 6, 4 years old he has know for 4 years.. he has always taken all 3 them up until he got a girlfriend 6 months ago now he files for a divocre and doesn't want the inconvience

We are in Ohio and he had the paternity test done 4 years ago the children are 4 ,6 and 8 yrs. The only reason he has for doing this is his new GF she does not want to be bothered with our kids she rarely has her own son

Sorry but Ohio law is with your husband on this one (See Establishing Ohio Paternity (http://www.daytondivorcehelp.com/establishing_paternity_ohio.php)) If there is "clear and convincing evidence" that he is not the father, i.e. DNA evidence then his paternity will be rescinded and his responsibility ended. He is well within the time frame to file such an action since he has until the child is 23. So he is very likely to win his petition.