It is haraam to take out a riba-based loan to buy a house or anything else. You did well to refuse to do that and advise your parents accordingly.
The one who takes out a riba-based loan should pay back the original money, but he is not obliged to pay the interest unless he is compelled to do so. It is permitted for him to use trickery to avoid it.
Based on that, if your father's aim in filling out this form is to reduce the debt or interest, then there is nothing wrong with it and there is nothing wrong with your filling out the form. But if the aim is to get involved in more riba, or to extend the loan period with an increase in interest, in this case it is an interest-based transaction, and it is not permissible for you to help your father with this transaction, because Allah, may He be exalted, says (interpretation of the meaning):
Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment
But if not submitting this application will result in him going to jail, in that case it is permissible for him to submit it because it is a case of necessity, and it is permissible for you to help him with it.
See also the answer to question no. 99149
And Allah knows best.
Reproduced from Islam QA