In most cases it's enough to say "брак" (marriage). "Совместный брак" is used to stress that the marriage is between those two people in question (but it sounds rather formal).

eg.
Гадалка сказала, что Антон и Таня будут несчастливы в браке = A fortune-teller said that Anton and Tanya will be unhappy in marriage (it's unclear what marriage is meant)
Гадалка сказала, что Антон и Таня будут несчастливы в совместном браке ~ A fortune-teller said that Anton and Tanya will be unhappy if they marry each other