enquiry regarding house benefit pls

HI all, am here to seek advice regarding applying for housing benefit.
My wife who is dual citizen Irish/British as mum is from Ireland, father is british from Northern Ireland. Born in Northern Ireland.
Currently we applied for EEA2 which is still under consideration. Wife used to work full time but after her maternity leave she decided to continue with part time as I was working full time and pay the rent but now un-employed. So we re considering going for housing benefit, will it be classify under public fund? Any advise will be helpful thanks in advance.