Nat,
Does he sign-on for U. Benefit or U. Assistance. If UB, then the only change is he will lose the Adult Dep. Rate on his claim - it's possible he is not gettig this for you anyway as you are already working. If you are working and Registered for PRSI to get "stamps" then you are already registered for tax. It's possible you are not getting taxed due to your income below certain limits.
If doing Self employed work as well as PAYE then you complete a Self-Assessment TAx form to record your earnings.
If your household income is low it may be possible to qualify for Family Income Supplement (FIS). Your weekly hours in employment would have to be 19 hours.
Check website welfare.ie and look up Families and Children then Family Income Supplement.
Contact your local Citizens' Information Centre, MABS or the INOU (Irish National Organisation for the Unemployed) they will do calculations for you to check your best options and you don't have to be unemployed to avail of their service.