The award is given annually to the book considered to best capture the comic spirit of PG Wodehouse.
This year marks the first time in the prize's history that it has been split between two winners.
Rothschild and Murray beat off competition from former winner Marina Lewycka, formerly shortlisted John O'Farrell, and US author Paul Beatty.
It is first literary award for Rothschild, whose book The Improbability of Love was her debut novel.
She said: "To use a word that my hero PG Wodehouse invented, I am terribly 'gruntled' by winning this prize, sharing it with the great Paul Murray."
The Improbability of Love is about the skulduggery of the London art world.
The judges described it as "a wonderful satire on the art trade, preposterous billionaires, Russian oligarchs and much else, a brilliant conceit faultlessly carried off".
Paul Murray's third novel tells the story of two Dubliners: Claude, a banker who decides to rob his own bank and struggling novelist and crook, Paul, who helps him do it.
The author said he was "delighted and honoured" to win the award.
"I first read PG Wodehouse as a boy and have kept returning to him ever since, longer than any other writer - which makes this award very special," he added.
The judges said: "Murray's setup is funny, the elegant zip of his sentences make you smile, his novel is an achingly topical, clever, delightful tale of folly and delusion. We loved it."
As with previous winners, Murray and Rothschild will be presented with a locally-bred Gloucestershire Old Spot pig - named after winning novels - at the Hay Festival on 4 June.
The prize was judged by a panel including Hay Festival director Peter Florence, Everyman's Library publisher David Campbell, writer and comedian Sara Pascoe, and BBC books editor James Naughtie.
Naughtie said: "It was impossible to separate these two books, because they made us laugh so much.
"Between them they produce a surfeit wild satire and piercing humour about the subject that can always make us laugh and cry. Money."
The winners were announced ahead of the Hay Festival which begins on Thursday.
Previous winners include Alexander McCall Smith, Howard Jacobson and Sir Terry Pratchett.
Authors Paul Murray and Hannah Rothschild have jointly won the Bollinger Everyman Wodehouse Prize.