Spouse visas will state “No Recourse to Public Funds” as do many other visas. For claiming tax credits the British national (or settled national) s permitted to make an application for working tax/child tax credits. These applications require both parents names on the application, but this doesn’t count as the non-eea national claiming a public fund. Child benefit is not classed as breaking the “no recourse to Public Funds” rule either.
Exception for couples
Where one member of a couple is subject to immigration control and the other is not, or comes within one of the exceptions above, a joint claim can be made and both claimants will be treated as though neither is subject to immigration control. However, the second adult element of WTC will generally not be awarded.
You can read more here
http://revenuebenefits.org.uk/tax-credits/guidance/how-do-tax-credits-work/who-can-claim/#Subject to immigration control