My husband and I have a joint motgage with another couple for a beautiful apartment in the Algarve.
One of the party has defaulted on two payments so far and intends to decline future payments.
If we make the payments on their behalf, will they continue to have full legal rights over their share?
Are we protected in any way by Portuguese law?

Not sure about Portuguese law, But I suspect you would be able to sue them for not holding up their end of the agreement. You can sue them for the payments they reneged on or for them to sign over their share to you.