My fiancé and I both pay our mortgage and this includes interest. Can we both claim the interest on the 1098?

No. 

You both cannot claim more than the interest listed on your form 1098. If you both paid the mortgage, then you should divide the interest between you.

CO-OWNING A HOME

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/deduct-mortgage-interest-co-owned-home/L6yLU1kKI_US_en_US?uid=lrv7xcw2