FHA's published rules allow your minimum required investment to come from gifts and from secondary financing provided by governmental bodies and approved nonprofits — which is precisely what most down-payment assistance is. Conventional loans have parallel rules (Community Seconds). So "assistance + mortgage" is a normal, designed-for combination, not an exception.

The catch is that BOTH sides must accept the pairing: the assistance program's lien terms must satisfy the mortgage's rules, and the lender must actually work with that program. Some pairings also stack with each other (a state program plus a county program); each program's own rules say whether.

The efficient question to a lender is: "Which of these specific programs do you close with?" — and to a program: "Which participating lenders should I call?" Both lists exist; make them give you theirs.