The father came under suspicion after the 16-week-old baby's death last year and the baby's identical twin was removed from the family home.
Social workers highlighted the fact that the twins' older sister, named only as K, had been taken to hospital with a serious head injury in 2011.
They argued that the father and the children's mother 'knew more than they were saying' about how K suffered a fractured skull.
But Mr Justice Peter Jackson ruled that the parents were not responsible either for K's injury or for the death of her younger sister, L. The judge ordered that both K, now three, and the surviving twin be returned to their parents' care.
Describing the couple as 'very close, intelligent, hard-working and aspirational', the judge said they were of good character and deserved to be believed.
Social workers claimed that L 'probably died as a result of her father lying on her when he was sleeping on the same sofa'.
It was suggested that the father had covered up the baby's 'accidental suffocation' by placing her in her rocker after her death.
The mother accepted that the twins' sleeping arrangements on the night of L's death was 'not the greatest idea'.
But the couple otherwise disputed every part of the council's case during an eight-day High Court hearing.
The judge said that a post-mortem examination had recorded the cause of L's death as 'unascertained'.
He conceded that the parents' account could not be 'accepted without question' and 'acknowledged the possibility that they have put their heads together to cover up a case of overlaying'.
But he ruled: "For the father to have placed L in her rocker, knowing that she was moribund, and then gone to bed would be extremely out of character. There is no reliable evidence that he did this.
"My conclusion is that we simply do not know when or why L died. Nor has it been proved that either of the parents knows.
"A finding against the parents would be based on speculation or suspicion, which would be impermissible and wrong."
He added: "The sleeping arrangements that were made for such small babies were obviously unwise, but that does not cross the threshold for intervention."
The council insisted that one or both of the parents knew how K was injured, but that they were intent on 'concealing' the truth.
However, the judge said: "With some hesitation I find that the parents' account of events can be accepted.
"I cannot conclude that it is more probable than not that they are concealing a known incident."
The judge concluded: "I therefore find that the grounds for making care orders do not exist. In consequence, the children will return to the care of their parents".
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