Meredith Katharine Borowiec, 30, has been charged with second-degree murder in the deaths.
Investigators say they were born in 2008 and 2009 and died shortly after birth. In October 2010, the third baby was saved from the garbage bin and the investigation of that case led police to lay the murder charges.
"I think any time you have a case such as this, it is shocking," said Calgary police Staff Sgt. Kelly Campbell. "This doesn't happen everyday and it's unfortunate that this did happen."
Campbell would not say what police think happened to the two dead children.
"It'll be highly unlikely to recover the bodies due to the length of time of not knowing where these bodies are," she said.
The necessary evidence to lay the charges was gleaned through witness interviews, Campbell said, though she wouldn't elaborate. Borowiec has been co-operative throughout the investigation, she said.
"I can't give the details as far as how, but it was suspected that she was pregnant. That was from information from witnesses."
The story of the baby found in the dumpster was gripping because the baby's father played a part in the rescue, apparently not knowing that the child was his.
The father, who told police he didn't know his girlfriend was pregnant, was on his way home in October 2010 when he and other passersby heard crying coming from the trash bin.
They jumped in and found the infant in a garbage bag.
Police and EMS workers were called and the baby was taken to hospital.
Borowiec was charged with attempted murder, criminal negligence causing bodily harm, child abandonment and failing to provide the necessities of life for a child under 16.
Campbell said officers can't confirm who the father of the other two children is because the bodies have not been recovered.
Police say Borowiec doesn't have any other children.
The child that was found in the dumpster has recovered and is healthy, Campbell said.