If he is actually actively looking for a job (rather than just waiting to see if one falls into his lap) then he should claim JSA. He will have to enter into a jobseekers agreement with the Job Centre. He can then end the JSA if/when he starts his self-employed work with you.
If you are already getting tax credits, you need to tell them he is no longer working, & if he claims JSA tell them that. His JSA may be Contribution Based (which is not means tested) if his NI record is suitable, & tax credits should be told that as well. Then if/when he starts as self-employed tell them that & give an estimate of his likely income for the 12-13 tax year.
If he is not entitled to contribution based JSA then he may not get any, as the alternative (income based JSA) is means tested & your income would be taken into account is working out whether he had any entitlement.