Lauren
Contribution ESA is no longer available for new claims, however, you might be able to claim New Style ESA which is the UC equivalent.
You will need to have a minimum of 50 weeks of NI Contributions in the Tax Years 2016-17 and 2017-18.
If you don't have the required NICs, then your only choice is to claim Universal Credit and as you have posted this will be as a couple.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems