The requirement from UKBA is principally to demonstrate that you have been living together at the same address (and still do) throughout the 2 years probationary period.
If you take a look at the ILR application form the UKBA do provide some of the most common examples.
The documents can be joint names, individual names or a complete mixture.
There's really no strict set of documents.
Caseworkers must base their decision on "the balance of probability" and according to what you have stated. The probability is that you live together.
Here's a typical listing of documents that have been used successfully:-
Driving License
TV License
Electricity Bills
Gas Bills
Water Bills
Council Tax Letters/Bills
Bank/Building Society statements
Bank/Building Society letters
Marriage Certificate
Registry Office Letters
NHS medical cards
Letters from GP/Medical Centre
Sports club membership cards
Insurance Quotes
Letters from Church Organisations
National Insurance appointment letters
HMRC Communication/Letters (eg Tax Codes, P60's etc)
Personal letters from friends/family etc
Telephone/Internet bills/letters/statements
Mobile phone bills/letters/statements
Online shopping details of name/address
Tenancy agreement(s)
Letters or other documents from government departments or agencies.
Letters from Dept of Work and Pensions, DVLA etc
Letters from UKVI / Home Office
I'm sure there's many more......
Keep thinking and good luck