Thanks for your patience.
At the end of the residence card you hold you can apply for Permanent Residence which is confirmation that you are allowed to remain in the UK free of immigration time restrictions. You can only apply for this if you have been continuously working during this time. Similarly your husband must have been exercising a treaty activity which means either working or studying. If there was a prolonged period where he was doing neither then your application may be rejected.
This is what you should apply for before you visa expires.
You can apply for PR using Form EEA4. Here is the link to the form on the UKBA website:-
You will have to send all the supporting documentation you have correctly identified (payslips, tax returns, tenancy agreements etc).
Once you have PR you can apply to be naturalised as a UK citizen 12 months after you have held PR. Here is the link to the information you will need to do this:-
You can only apply for naturalisation if you meet the residenctial criteria in terms of times spent in the UK and you will have to check that you are eligible with regard to the potential days absent resulting from your husband's continental work at the time:-
Once you have UK citizenship you cannot lose it. If you only have PR then this can be revoked after 6 months outside the UK.
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