Angela Cannings is the latest in a series of high-profile cases regarding infant deaths.
Terry Cannings has supported his wife throughout the case
In January, solicitor Sally Clark, who had been jailed for murdering her two baby sons, was cleared by the Court of Appeal.
Three judges decided that her conviction was unsafe.
And in June, 35-year-old pharmacist Trupti Patel was cleared of murdering her three babies by a jury at Reading Crown Court.
Angela Cannings was jailed for life in April 2002 for the murder of seven-week-old Jason in 1991 and 18-week-old Matthew in 1999.
She denied this, claiming that the boys were victims of sudden infant death syndrome (SIDS) or cot death, due to a genetic defect.
Trupti Patel was cleared in June
Her legal appeal has been based on several factors, but principally that the expert evidence of Professor Sir Roy Meadow - who was also involved in the Sally Clarke and Trupti Patel cases - was misleading.
Michael Mansfield QC argued that, were the trial to take place now, "it is unlikely the Crown would call Professor Meadow as a witness, or, if they did, it would have to be done with a health warning attached to it".
He recalled that the Court of Appeal had made strong observations about Professor Meadow's evidence in the case of Sally Clark.
When Ms Cannings was convicted, the jury was told that the deaths of her children could not have been caused by a genetic defect because there was no evidence of other infant deaths in her close relatives.
But information gathered by the BBC's Real Story programme showed that her great-grandmother and grandmother, had also lost babies in unexplained circumstances.
An expert on medical statistics, Professor Robert Carpenter, also said that Ms Cannings' sons had been laid to sleep on their front, and may have been exposed to cigarette smoke - both factors which gave them a higher chance of SIDS.
All three of the recent cot death cases have served to highlight the difficulties for police investigating the sudden and unexpected deaths of infants.
The trials have also highlighted one of the main obstacles to proving a case
against a mother accused of killing her own babies - that of motive.
The government has now ordered a review of the procedures used for
investigating mothers accused of murdering their own babies in an attempt to
better resolve some of these issues.
And the Crown Prosecution Service has said it will look at whether to review
past cases involving certain medical experts, including Professor Meadow.