My husband had an affair,still the other women was married and she says that my husband is the father of the child. She had her husband believe that he was the father and he sign the birth certificate and was under his medical insurance, its been 3yrs later the woman is calling my husband telling him that she is going to take him to court for child support and DNA. Even if her husband sign the birth certificate can my husband be held responsible after 3yrs?

If the DNA test proves its his... YES. And personally I would insist on a DNA test.

But it helps to know what state because its not handled exactly the same in every state.

It can depend on the state where you live ( if in the US)
In some, anytime up to the age of 18 she can also contest the paternity and ask for a DNA test.
In others since she was married, the husband is considered the father regardless and she can't come after your husband.

In most she has a limited time to contest the paternity,
So yes there is a good chance she can, and to be honest I would think your husband would want to know and he would be the one asking for a DNA test.

My husband had an affair,still the other women was married and she says that my husband is the father of the child. She had her husband believe that he was the father and he sign the birth certificate and was under his medical insurance, its been 3yrs later the woman is calling my husband telling him that she is going to take him to court for child support and DNA. Even if her husband sign the birth certificate can my husband be held responsible after 3yrs?

It will depend on your location.There is deadline for paternity contest in some states.Other states allow paternity disestablishment to be done at any time.

It depends on the state. In some states, 3 years is too long. In other states, you have until the child is 18 to challenge.

Where are you?