Charlotte Bevan, who had schizophrenia, walked out of St Michael's Hospital in Bristol in December 2014 with daughter Zaani Tiana Bevan-Malbrouck.
Their bodies were found in undergrowth in the Avon Gorge days later.
The serious case review also found the lack of a lead clinician overseeing Ms Bevan's care led to confusion.
The Bristol Safeguarding Children Board's report said there was a system for controlling entry to the ward "but mothers and babies were allowed free access throughout the hospital".
It went on to say that, "this allowed CB [Charlotte Bevan] to leave the ward with ZBM [Zaani Tiana Bevan-Malbrouck] unnoticed and unchallenged".
The report said once the alarm was raised that Ms Bevan and her four-day-old daughter were missing, there was a quick response.
However, it said the safeguarding concerns were "everybody's business" as Ms Bevan was "able to walk outside at night, in unsuitable clothing, carrying a newborn baby, in a public place unchallenged by anyone".
Since their deaths, the report said ward security had been "reviewed and improved" and changes had been made to the reception area.
Charlotte's mother Rachel Fortune, who contributed to the review, said in a written statement "no single thing, action or person was to blame".
In the statement, released jointly with her daughter Janet, she said there were eight main findings which offered "clear, constructive learning", including how to manage long-term mental health in pregnancy, "honest, accurate and timely communication" and how several agencies could work together with a lead clinician.
She added: "This was a particularly difficult case to manage as long-term ill mental health and pregnancy came together. It's our hope now that any families and individuals facing such difficulties will have a multi-agency team with accountable clinicians in each service, as they now do in Bristol."
The review also found Ms Bevan's explanation for stopping her medication due to breastfeeding concerns was not followed up with a pharmacist until after she had given birth.
She later revealed she had not been taking medication for the last five months of her pregnancy, which the review team speculated was a sign of "disguised compliance".
The report said: "It is notable that it was not until CB [Charlotte Bevan] had given birth to ZBM [Zaani Tiana Bevan-Malbrouck] that any professional contacted a pharmacist to confirm the safety of her medication on ZBM when breastfeeding or otherwise."
There was also confusion over who was leading, co-ordinating and overseeing Charlotte's overall care, the report found.
In some cases, it found, health professionals assumed it was the Mother and Baby Unit Doctor, the mental health care co-ordinator or her GP.
The report also found there was confusion over the terminology in describing her mental health condition. It found that describing her as "well" meant there was no clarity in what this meant in mental health terms.
Independent chair of the Bristol Safeguarding Children Board, Sally Lewis said: "This review provides constructive learning for many agencies and professionals working in Bristol and beyond.
"A great deal has already changed in local professional practice since this tragic incident, some of which has been influenced by the findings of this review and has been noted by the Board in our formal response."
A mother who jumped off a cliff with her baby was able to leave a maternity ward unchallenged as she had "free access" in the hospital, a report said.