Hi @Phiona
As you say the Sozialamt is paying your health insurance, are you an asylum seeker? If so, you cannot receive assistance from the Jobcenter. You can register as a job seeker with the Agentur für Arbeit and ask them to fund the course. You need an education voucher (Bildungsgutschein) from the Agentur für Arbeit to pay the cost of the course.
The DCI states on its website that they accept the Bildungsgutschein from the Agentur für Arbeit or the Jobcenter.
If you are not an asylum seeker, then I do not understand why the Sozialamt is paying for your health insurance. Firstly, it generally for people who are retired or unable to work. Secondly, if the Jobcenter says you earn enough as a family to pay your own health insurance then the same rule should apply with the Sozialamt.
If you are able to work and not an asylum-seeker, the Jobcenter is responsible. Even if a person or family have enough income to pay their other costs but cannot afford the health insurance contributions, then the Jobcenter has to cover this cost.
Best,
Éanna