Praise be to Allah.
If the matter is as you describe, there is nothing wrong with you taking this loan, because it is a goodly loan without interest. The fact that the one who is lending it to you -- which is the department in question -- has borrowed this money with interest, does not affect you, because you are not dealing with interest and because the one who takes a loan with interest takes possession of the money that he borrows, according to the more correct scholarly view, and it is permissible for him to dispose of it by giving it or lending it or otherwise, even though he is committing sin by dealing with riba.
See: al-Manfa’ah fi’l-Qard, by ‘Abd-Allaah ibn Muhammad al-‘Imraani, p. 245-254
We ask Allaah to make things easy for you, to meet your needs and to bless you in your livelihood.
And Allaah knows best.