Typically, if both people are liable for paying the mortgage, then the mortgage interest deduction may be split in whatever manner you want as long as you are not deducting more than the total that was paid.
The TurboTax article below states that each person must deduct only the portion that they paid. You mentioned in your question that both parties contribute to the bills of the household, so as long as the party who is deducting the mortgage interest has contributed at least as much to the household to cover the mortgage interest, then they should be able to deduct it and provide documentation to the IRS showing they paid with their funds (in the very unlikely event that it is examined by the IRS).
Here is the article that explains some different situations for deducting mortgage interest:
How do I deduct mortgage interest if I co-owned the home?
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