Bain was acquitted of the 1994 murders of his five family members on Friday in one of the most controversial criminal trials in New Zealand history.
One juror hugged Bain outside the Christchurch Court House and two attended a post-verdict celebration party.
The Herald on Sunday reported one juror later admitted it was inappropriate to attend the party and they left shortly after arriving.
However, they still wanted to meet the man they freed, he said.
In another unusual move, a female juror also approached the paper and spoke about the enormous pressure the jury panel was under during the 13-week trial.
Bain's defence lawyer, Michael Reed, QC, told The Press it was "entirely understandable" for jury members to want to meet the subject of their deliberations.
He said the juror's interview was also understandable because it highlighted the burden of jury duty.
"I think it was quite nice to hear how they were suffering; how they feel, the abysmal way they are paid and how they suffered financially.
"I would be in favour of more openness with a jury and finding out what's going on."
If the jurors had talked about deliberations to the media they could be charged with contempt of court, said Chris Gallavin, a senior law lecturer at Canterbury University.
He said some of the jurors' behaviour was unusual, but so was the case.
"I can imagine at the end of it they might be feeling relieved, elated and pretty emotional," Dr Gallavin said.
Opposition justice spokesperson Lianne Dalziel told Radio New Zealand the jurors should have been held together for a debrief and kept well away from the trial participants.
There needed to be a review of the way jurors were briefed and how well prepared they were for major trials, she said.
