A father has been charged with sexually assaulting his baby daughter and offering her up to his boyfriend, who then gloated about it over Skype.

The two men, both aged 50, were arrested in Ivanhoe, Victoria on Tuesday. They were extradited to Sydney on Wednesday night to face charges that Child Abuse police said were so horrific they were lost for words.

Neither man appeared in Waverley Local Court on Thursday when their matter was briefly mentioned.

It's understood the men, who cannot be identified for legal reasons, are in a relationship and live together in Melbourne.

One of the men fathered the little girl, who was born in 2014 and now lives with her mother in a small town in central western NSW.

It's alleged the men travelled to the town on April 19, 2015 and looked after the baby girl for three hours while her mother was at a training course.

Unbeknownst to her, the men allegedly sexually abused the 10-month old baby over those three hours and allegedly took photos of her that they later uploaded to their computers.

Police will allege that, in a Skype conversation two days later, the father's partner spoke to an associate and said: "Her mother was out for a while. We did not have enough time to do everything that we wanted to unfortunately."

He also allegedly said: "I want to drug the little one and really have a good time."

He didn't specify whether the mother knew what had happened but allegedly said: "the mother is a f--king bitch though...& I hate her".

Some of the other comments he allegedly made are too disturbing to publish.

In a Skype conversation with another associate prior to the trip in April 2015, he allegedly said that they were "going away to play with the baby for a few days".

"[The father] and I will have time on our own with her," he said. "Incest turns me on so much."

Victorian police searched the home of one of the associates in March this year and, after searching his computers, found material that prompted them to search the Ivanhoe home of the two 50-year-old men.

There, they found terabytes of material on their computers including images of the baby girl and Skype conversations.

Detective Acting Superintendent Peter Yeomans, commander of the Child Abuse Squad, was lost for words to describe how horrific the allegations were.

The father has been charged with two counts of sexual intercourse with a person under ten years and the production, possession and sharing of child pornography.

His Legal Aid lawyer said he will be represented by the Aboriginal Legal Service at his next appearance in Central Local Court on Tuesday.

The father's partner has been charged with sexual intercourse with a person under ten years, as well as further child porn-related offences and use of a child under 14 years to make child abuse material.

They were both refused bail.