The England captain has been beset by rumours of a fling with his former personal assistant, Rebecca Loos.
The 26-year-old worked for him as he settled into life in the Spanish capital after his move to Real Madrid last year.
She worked for the SFX Group, the sports management company which looked after the Beckhams.
Reports of the alleged affair broke in Sunday’s News of the World, but Posh and Becks looked happy and playful in snaps taken at the start of a holiday in the ski resort of Courchevel in the French Alps.
And in her first comment on the scandal, Posh said: “We have been through a lot worse than this, and we’re definitely going to get through this.”
The 28-year-old soccer star met with his family in Switzerland on Monday, a day after labelling reports of the affair as “ludicrous”.
The midfielder will spend a couple of days with his family in what sources said was a pre-planned break.
In his statement on Sunday, Beckham said: “The simple truth is that I am very happily married, have a wonderful wife and two very special kids.
“There is nothing that any third party can do to change these facts.”
The News of the World, which also published explicit text messages which it claimed were sent between Beckham and his then-employee, has stood by its story “100%”. It is not known if Beckham is considering legal action.
England coach Sven Goran Eriksson refused to comment on the allegations.
The reports claimed Beckham invited Ms Loos to his Madrid hotel room on September 18 last year after a night out drinking.
This was reported to be one in a series of four meetings, before the footballer broke off both his relations with SFX and with Ms Loos last December.
The newspaper said he never saw her again but the text messages were reportedly sent between the two as recently as last month.
The alleged revelations were told via a “family friend” of Ms Loos.