As I understand it, you are as a family receiving some money from the Jobcenter.
If you wish to take part on an integration course, you can do this by applying for permission to do so from BAMF. As you are working, you'll have to try and find a part-time course. Here you can search for a language school oferring the integration course in your area:
If you are getting help from the Jobcenter, you do not have to pay for the course.