Can we travel from one state to another with my husband's approve I-130 and his driver license?

More information is needed. Did he enter the U. S. with a visa? Has he filed for adjustment of status? The I-130 petition will not prevent him from being questioned, nor does it prevent someone who is unlawfully present or an overstay from being placed in deportation/removal proceedings. As a result, I strongly recommend an appointment or teleconference with a competent and experienced immigration attorney, before there are any more complications.

An approved I-130 petition does not create authorization to be lawfully present in the U.S. A pending I-485 Application for Adjustment of Status can make it lawful for the beneficiary to remain in the U.S. while that application is pending. It would be wise for you and your husband to consult with an immigration attorney about this matter, and also about the filing of an I-485 (with applications for an Employment Authorization Document - sometimes called a "work permit" and for Advance Parole - sometimes called a "travel document") if those applications have not yet been filed. After learning all of the relevant information about your husband, his immigration-related history, etc., an attorney could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.