External experts reviewed the deaths, which occurred at Royal Oldham Hospital and North Manchester General Hospital between January 2013 and July 2014.
They found a "notable absence of clinical leadership" resulting in a "failure to adequately plan care".
Pennine Acute NHS Trust apologised to the families of those who died.
A trust spokesman said he could not comment on whether any of the deaths resulted from failings, saying it was a "legal matter for the coroner".
The review, carried out by a senior midwife and an obstetrician outside the trust, found risk management during and before labour were "below standard, which may have contributed to the poor outcomes".
Three cases involved women medically classed as obese, with their needs "not managed in line with local and national guidance".
Twelve recommendations were made, including improving how serious incidents were dealt with and reviewing the process for employing locum doctors.
Three maternal deaths "did not appear to be the result of deficiencies in care".
The trust said it was investing more than Â£1m by recruiting 40 new healthcare assistants to support patients and midwives.
Thomas Beaty was one of seven babies who died. His parents earlier said they believed he would still be alive "if it were not for the actions of Royal Oldham Hospital".
He suffered severe head injuries after five attempts were made to deliver him using forceps.
National guidelines recommend no more than three attempts.
Gill Harris, chief nurse at the trust, said the incidents "should be seen in the context of approximately 10,000 births a year" at the hospitals.
She said: "The trust board today repeated sincere apologies to all of the families involved for the failings in care which had been identified. I have met with a number of the families and have reiterated the offer to meet with the remaining families, if they wish.
"The review of the incidents found that whilst the maternal deaths did not appear to be the result of deficiencies in care, further scrutiny and improvement was required from the review of the neonatal deaths."
The trust will now be twinned with the Newcastle upon Tyne Hospitals NHS Foundation Trust as a "shared learning arrangement".
A review ordered after the deaths of seven babies and three mothers has led to urgent changes at two Greater Manchester maternity units.