The brothers say their bandmates - Tony Hadley, John Keeble and Steve Norman - became their "second family" after their parents died within 48 hours of each other in January.
Guitarist Gary said: "I think I coped and my brother did too because of the band. It was like having another family to catch us. I think they understood what we were going through.
"They knew our parents very well. They were moved by it and they supported us."
Eileen Kemp was undergoing heart surgery at Bournemouth hospital when her husband Frank had a fatal heart attack. Eileen died shortly afterwards.
Bassist Martin told Britain's Hello! magazine: "It came as a tremendous shock. They spent 50 years of their lives together. My dad wouldn't even go down to the pub with me because he wouldn't leave my mother on her own.
"That's how close their marriage was. The fact that they went together was in some ways comforting. Like it was meant to be. That's how I came to see it and that helped me deal with the loss."
The group - who officially reunited in March this year - split up in 1989 and spent the next 20 years in bitter conflict, with Tony, John and Steve suing Gary over royalty payments in 1999.
They eventually reconciled and kicked off their reunion tour in Dublin earlier this month.