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Couch and Barrow totalled 321.24 from five dives in the synchronised 10m platform final, with China winning gold (337.14).
Gallantree and Starling scored 302.88 in the synchronised 3m springboard event to finish behind China (322.40) and Italy (306.90).
It is the first event at the London Aquatics Centre since the 2012 Games.
Great Britain's Couch and Barrow, who finished fifth at the Olympics, led the standings after the first two rounds, where the difficulty of the dives performed is restricted.
However, four-time Olympic champion Chen Ruolin and her 2013 world championship gold medal-winning partner Liu Huixia edged ahead in the third round and could not be caught. Canada finished third with a total score of 316.11.
"We really enjoyed the competition and it's great to be back," Barrow, 25, told BBC Sport.
"The result means we're the leading pair in the Commonwealths, so that's a big confidence boost ahead of Glasgow this summer."
Couch, 24, added: "I had a bad injury (dislocated knee) at the beginning of the year, but we have come back strong and came here today thinking 'let's do it' and the support from the crowd really helped us."
We really enjoyed the competition and it's great to be back
Gallantree, 29, is usually partnered by Alicia Blagg, but she missed the event through injury and Starling, 18, was only drafted in last week.
"I'm so proud of the way we dived today," Gallantree told BBC Sport.
"We haven't had much time together and have only dived as a pair once before back in 2012 so it's a great result."
Starling added; "It's my first international medal which means I'm not the only one of the team without one anymore so I'm delighted."
The men's synchronised 3m springboard final was another event won by China, but new British pairing Jack Laugher, 19, and Chris Mears, 21, impressed by coming fourth.
"Although it's frustrating to come so close to a medal we have to be so happy about how we dived today," said Laugher after finishing 11 points off the podium positions.
Mears added; "It's the pairing we've wanted for a while and it's so great to be diving out there with my best mate and I think we can go on to do big things together."
With Tom Daley currently without a synchronised diving partner, Dan Goodfellow, 17, and Matty Lee, 16, were the British competitors in the men's final.
They had won two successive World Series bronze medals since making their debut as a pair earlier this year, but despite recording a personal-best of 403.86, finished fifth.
China secured gold with 479.13, while Ukraine (448.26) and Germany (425.82) filled the other podium positions.

16 March 2015 Last updated at 14:20 GMT
The Green Lantern ride at the Movie World park on Australia's Gold Coast stopped after a wheel broke.
It became stranded 50 metres off the ground and took fire crews to take 3 hours to get the people down safely.
No one was hurt - and you can see the clip of the rescue mission above.
Tonia Couch and Sarah Barrow won World Series silver while Rebecca Gallantree and Hannah Starling took bronze.
[NEXT_CONCEPT]
Six people had to be rescued after a rollercoaster in Australia got stranded 50 metres in the air.