Reports recently emerged that their relationship was on the rocks following a series of heartfelt messages on Twitter that hinted at strains.
But Danni Minogue and boyfriend Kris Smith have released a statement insisting they are "happy".
"Thanks for your concern. We're happy to be back at home in Melbourne together as a family," the statement read.
"We are committed to our relationship and Ethan as always."
Earlier in the week, Danni and Kris took to Twitter to post a series of meaningful messages that have since been deleted.
"Never chase love. If it isn't given freely by another person, it's not worth having," 39-year-old Dannii wrote.
And in another message, she said: "Forgiving someone does not mean forgetting what they did. It simply means letting go of the hurt."
Kris, 32, also hinted that they were going through a rough patch, saying: "You don't know what you've got til it's gone."
The couple met in Ibiza in 2007 and have 10-month-old son Ethan.
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