my husband and i have a daughter together. he is not her biological father
Then you and your husband do NOT have a daughter together. The biological father has rights, too, regardless of the fact that you tried to defraud him of those rights.
but has took on full responsibility for her and signed her birth certificate. her biological father has now decided that her want to take full custody of her. i was wondering who has legal rights to her?
He will first have to establish paternity, but it's pretty easy to get a court order for that.
He will then file for custody and/or visitation. You didn't give your daughter's age, and that will be important. Dad might get joint legal custody, but it's extremely unlikely (essentially impossible) for him to get sole legal custody unless you are horribly unfit or your husband is a convicted child abuser. Whether dad gets joint legal custody or not, he will be able to ask for visitation - and will receive it. There may be some graduated visitation schedule.
Note, however, that you run the risk of messing everything up for yourself. If you continue pretending that your husband is the father, then it COULD cause you to lose legal custody. So stop doing that. The child is entitled to know her father.