Allegations surfaced yesterday that Marsh's fiancé Jamie Lomas was unfaithful after carer Katie Moores claimed he invited her back to his hotel room.
However, the couple have vowed to "work through" and "talk through" their issues, according to The Mirror.
"They are still living in the same house and that says a lot," a source said.
Appearing on yesterday's BBC Breakfast, Marsh said about her private life: "You just get on with it don't you really, it's just part of the job. It's tricky."
Marsh, who plays Michelle Connor in Corrie, last month denied rumours claiming her relationship with Lomas had collapsed.
They have been together since 2008.