Other may chime in but I believe a joint mortage means both parties are resonsible for the full amount so I think your DTI is correct as they said.
I've never had a mortgage so I don't know directly but I do know 2 people who were denied car loans due to mortgage DTI issues and they were joint mortgages.
Even 35% is pretty hefty considering that anything over 40% is "high risk" to some lenders.
The 2 people I know who were denied ended up getting predatory auto loans and were not happy with the outcome/payments.
Are you claiming your mortgage partner's income with your own? you are allowed to do so, you are expected to do so. Its why income is usually listed as
Household Income: |_____________|