You husband cannot claim UK tax credits on people who aren't: 1) British nationals 2) EU/EEA nationals 3) permanent residents (ILR) of the UK. Once you and your children get ILR, he can claim them. Till then, it's not legal.
Once you do get ILR, any claim for tax credits is based on joint income, no matter who applies.
Most people who work in the UK are PAYE - pay as you earn. There's no need to complete a tax return unless you are self-employed or work a job that is not PAYE.