He can apply for Child Tax Credit right now if he is in fact, the child's primary care giver.
Then, when you get ILR, you apply for Working Tax Credit.
It might get a little cockced up, b/c you'll have to re apply entirely since all tax credits are determined jointly, and in the interim they'll stop paying you till it's sorted, so be prepared for that.
As for housing benefit, it varies by council, but ours actually asks immigration status for both applicants if applying jointly.