Cops praised as slain Vic couple buried

The family of a couple found slain in their Melbourne home has thanked police for solving the case so quickly as they gather for a private funeral.

Robert Adamson, 65, and his wife Cheryl, 60, were found dead in Murrumbeena last month.

A 21-year-old neighbour was charged with the couple's murders about four days after their deaths.

The couple's family released a brief statement on Tuesday as friends and relatives gathered at St Peter's Church in Murrumbeena for the funeral.

"We wish to express our thanks to the community for the strong support received following the tragic passing of Cheryl and Robert Adamson," the family statement said.

"We also want to acknowledge the hard and swift work of Victoria Police."

Mr Adamson was an accountant and his wife the senior teacher librarian at Melbourne Grammar School's primary school, Grimwade House.

Ms Adamson's colleagues discovered the bodies in the southeastern suburbs home when she failed to show up for work.

The couple had lived in the home for decades.

Thomas James Hemming, 21, is facing two counts of murder and is being held in custody for a committal mention in June.